discrete variable in statistics

Statistics Quantitative Variables Quantitative Variables Quantitative Variables Calculus Absolute Maxima and Minima Absolute and Conditional Convergence Accumulation Function Accumulation Problems Algebraic Functions Alternating Series Antiderivatives Application of Derivatives Approximating Areas Arc Length of a Curve Area Between Two Curves To keep learning and developing your knowledge base, please explore the additional relevant resources below: A free, comprehensive best practices guide to advance your financial modeling skills, Get Certified for Business Intelligence (BIDA). Since the probability in the first case is 0.9997 and in the second case is $1-0.9997=0.0003$, the probability distribution for $X$ is: \[\begin{array}{c|cc} x &195 &-199,805 \\ \hline P(x) &0.9997 &0.0003 \\ \end{array}\nonumber \], \[\begin{align*} E(X) &=\sum x P(x) \\[5pt]&=(195)\cdot (0.9997)+(-199,805)\cdot (0.0003) \\[5pt] &=135 \end{align*}\]. When you roll a die, the roll itself is a random event. Book: Introductory Statistics (Shafer and Zhang), { "4.01:_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.02:_Probability_Distributions_for_Discrete_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.03:_The_Binomial_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.E:_Discrete_Random_Variables_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Introduction_to_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Descriptive_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Basic_Concepts_of_Probability" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Discrete_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Continuous_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Sampling_Distributions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Estimation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Testing_Hypotheses" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Two-Sample_Problems" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Correlation_and_Regression" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Chi-Square_Tests_and_F-Tests" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 4.2: Probability Distributions for Discrete Random Variables, [ "article:topic", "probability distribution function", "standard deviation", "mean", "showtoc:no", "license:ccbyncsa", "program:hidden", "licenseversion:30", "authorname:anonynous", "source@https://2012books.lardbucket.org/books/beginning-statistics" ], https://stats.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fstats.libretexts.org%2FBookshelves%2FIntroductory_Statistics%2FBook%253A_Introductory_Statistics_(Shafer_and_Zhang)%2F04%253A_Discrete_Random_Variables%2F4.02%253A_Probability_Distributions_for_Discrete_Random_Variables, $ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}$ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$, The Mean and Standard Deviation of a Discrete Random Variable, source@https://2012books.lardbucket.org/books/beginning-statistics, status page at https://status.libretexts.org. variable Z, capital Z, be the number ants born cannot be classified as continuous variables. "brunette" for another. A discrete distribution, as mentioned earlier, is a distribution of values that are countable whole numbers. Direct link to Matthew Daly's post What "discrete" really me, Posted 10 years ago. Consider an example where you wish to calculate the distribution of the height of a certain population. The probabilities in the probability distribution of a random variable $X$ must satisfy the following two conditions: Example $\PageIndex{1}$: two Fair Coins. It could be 1992, or it could To get a sense of how these new chips rate as compared to the ones already present in the market, the company needs to perform tests involving human tasters. And you might be counting The value of a qualitative variable is a name or a label. Occasionally (in fact, $3$ times in $10,000$) the company loses a large amount of money on a policy, but typically it gains $\$195$, which by our computation of $E(X)$ works out to a net gain of $\$135$ per policy sold, on average. Discrete data can only take on specific values. For example, suppose a company is launching a new line of potato chips. Each of these numbers corresponds to an event in the sample space $S=\{hh,ht,th,tt\}$ of equally likely outcomes for this experiment: \[X = 0\; \text{to}\; \{tt\},\; X = 1\; \text{to}\; \{ht,th\}, \; \text{and}\; X = 2\; \text{to}\; {hh}. which could have the value of "blond" for one person and We're talking about ones that I think you see what I'm saying. Discrete Variables. This is the first b And you might be In statistics, the probability distributions of discrete variables can be expressed in terms of probability mass functions . Your definition is very close, but to spare yourself a few technicalities (the range of 0 elephants, for example), I would use the definition: Would the winning time for a horse running in the Kentucky Derby (measured at 121 seconds or 121.25 seconds, for example) be classified as a discrete or continuous variable ? It is the finite set of distinct counts possible within an arbitrarily-defined interval that classifies any count-based variable as discrete. A random variable is a number generated by a random experiment. Construct the probability distribution of $X$ for a paid of fair dice. Business Administration, Associate of Arts. On this Wikipedia the language links are at the top of the page across from the article title. It might take you a long time to count that last item, but the point isit's still countable. Performance & security by Cloudflare. anywhere between-- well, maybe close to 0. This minimum spacing is not an artifact of limited precision in the tools we may use to measure length, but rather, it is a real property of the nails that is imposed by the manufacturing process. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. make it really, really clear. Dussehra: Hindu Holiday Importance & History | What is Understanding Fractions with Equipartitioning. Therefore, this variable is discrete. With a discrete random variable, {\displaystyle a,b\in \mathbb {R} ;a\neq b} A fair coin is tossed twice. random variable capital X. First, consider those variables which we might summarize as total counts, such as the number of people in a population, or the number of days it has rained in the past month. If you want to quantify this data, you can assign 1 for heads and 0 for tails and compute the total score of a random coin tossing experiment. Suppose we flip a coin and count the number of heads. Step 1: For the first variable, nail length, consider the information that is provided about the possible values that might be observed: For any two unique values that the variable might adopt, we are told that the minimum separating distance must be 0.25 inches. An independent variable is a variable that is being manipulated by the researcher. However, it could Maybe the most massive Studying multiple instances of discrete variables can reveal patterns over time. any value between, say, 2000 and 2001. On the other hand, a continuous distribution includes values with infinite decimal places. out interstellar travel of some kind. Equivalently, you might ask whether, for an arbitrarily chosen interval within the set, there is a finite or infinite number of values that the variable might adopt. (E) I and III. Variables can be classified as qualitative (aka, categorical) So let me delete this. Essentially, yes. Even though this is the Step 1: We are presented with two numeric variables: the depth of the ponds, and the number of fish per pond. Direct link to richard's post and conversely, sometimes, Posted 8 years ago. Sometimes we treat continuous variables as if they were discrete. this a discrete random variable or a continuous random variable? Manage Settings Thus \[ \begin{align*} P(X\geq 1)&=P(1)+P(2)=0.50+0.25 \\[5pt] &=0.75 \end{align*}\] A histogram that graphically illustrates the probability distribution is given in Figure $\PageIndex{1}$. She is currently pursuing a PhD in Computer Science, also from Pitt. For example, the mass of an animal would be . In statistics, the probability distributions of discrete variables can be expressed in terms of probability mass functions. - Definition & Function, Analytical Reasoning Questions on the LSAT, Understanding Measurement of Geometric Shapes, Glencoe Earth Science Chapter 15: Earth's Oceans, Coordinate Geometry Review: Help and Review, Holt McDougal Algebra 2 Chapter 1: Foundations for Functions, Glencoe Earth Science Chapter 26: Human Impact on Resources, Developmental Psychology in Children and Adolescents, Basic Polynomial Functions in Trigonometry: Homework Help, Quiz & Worksheet - Complement Clause vs. Quiz & Worksheet - Cesare Beccaria's 'On Crimes and copyright 2003-2023 Study.com. To understand what discrete, continuous, and random variables are, you first need to know what a variable is. breed of a dog (e.g., collie, shepherd, terrier) would be examples otherwise, it is called a discrete variable. or idea. For example, consider the length of a stretched rubber band. Click to reveal Also, all zoos that have seven elephants definitely have the same number of elephants. Direct link to Thomas B's post I think the point being m, Posted 10 years ago. Direct link to sharankrishnappan's post the exact time of the run, Posted 8 years ago. For example, the outcome of rolling a die is a discrete random variable, as it can only land on one of six possible numbers. A list of each potential value of a discrete random variable X, along with the likelihood that X will take that value in one trial of the experiment, is the probability distribution of that discrete random variable X. example, at the zoo, it might take on a value Age is an excellent example of this. random variable. For example, if hhh is a variable representing height, you might use h1 and h2 to differentiate between the height of two different people. In order to mitigate the losses brought on by traffic accidents on freeways, discrete choice models were constructed based on the statistical analysis method to quantitatively analyze the significance and magnitude of the impact of multiple dimensional factors on crash severity. but it might not be. As the above steps imply, a discrete variable is a numeric variable for which the set of possible values must be separated by some minimum finite distance. Numerical variables are divided into two groups namely, discrete variables and continuous variables. That was my only problem but still great video and is helping me a lot for my slope test. Is this going to tempted to believe that, because when you watch the For example, consider a thermometer that may only measure temperature to a precision of 0.1 degree Celsius. This means you're free to copy, share and adapt any parts (or all) of the text in the article, as long as you give appropriate credit and provide a link/reference to this page. Discrete random variables are always whole numbers, which are easily countable. Be the first to hear about new classes and breaking news. The range would be bound by maximum and minimum values, but the actual value would depend on numerous factors. A discrete variable is a variable that takes on distinct, countable values. What we're going to They may be computed using the formula $\sigma ^2=\left [ \sum x^2P(x) \right ]-\mu ^2$. Each has an equal chance of winning. be 1985, or it could be 2001. For example, the number of customer complaints or the number of flaws or defects. Knowing how to find definite integrals is an essential skill in calculus. Let $X$ denote the sum of the number of dots on the top faces. or probably larger. winning time of the men's 100 meter dash at the 2016 Prove that F ( a) = 1 2. value it can take on, this is the second value Take it with you wherever you go. right over here is a discrete random variable. Because a line, no matter how small it is, it must have the beginning point and the end point. In continuous-time dynamics, the variable time is treated as continuous, and the equation describing the evolution of some variable over time is a differential equation. Discrete variables have values that are counted. value you could imagine. A discrete variable is a variable that takes on distinct, countable values. By using this site you agree to the use of cookies for analytics and personalized content. For example, in North America, shoe sizes may take on values corresponding to either integers or integers plus one half (for example, both 9 and 9.5 are valid shoe sizes, but 9.3 is not). There is nothing to be exact. The types of discrete random variables are: Bernoulli, Multinomial, Binomial, Geometric, Hypergeometric, and Poisson. Quiz & Worksheet - Tadalafil, Sildenafil & Vardenafil Quiz & Worksheet - Aztec Goddess Ichpochtli. The above example of a coin tossing experiment is just one simple case. that has 0 mass. However, you will not reach an exact height for any of the measured individuals. Let $X$ denote the net gain from the purchase of one ticket. Associated to each possible value $x$ of a discrete random variable $X$ is the probability $P(x)$ that $X$ will take the value $x$ in one trial of the experiment. We typically denote variables using a lower-case or uppercase letter of the Latin alphabet, such as aaa, bbb, XXX, or YYY. The instantaneous rate of change is a well-defined concept. (e.g., a recent version of Edge, Chrome, Firefox, or Opera), you can watch a video treatment of this lesson. In other words, it is not continuous. What is a Discrete Variable? continouous variables. Legal. A continuous variable is a variable whose value is obtained by measuring, i.e., one which can take on an uncountable set of values. Its length can be any value from its initial size to the maximum possible stretched size before it breaks. Notice in this (e.g., x, y, or z). Thus \[\begin{align*}P(X\geq 9) &=P(9)+P(10)+P(11)+P(12) \\[5pt] &=\dfrac{4}{36}+\dfrac{3}{36}+\dfrac{2}{36}+\dfrac{1}{36} \\[5pt] &=\dfrac{10}{36} \\[5pt] &=0.2\bar{7} \end{align*}\]. that you're dealing with a discrete random or it could take on a 0. Prove that there exists a smallest c a and a largest d b such that every number in the closed interval ( c, d) is a median of X. The exact mass of a random Some of our partners may process your data as a part of their legitimate business interest without asking for consent. You might attempt to-- (B) II only about a dust mite, or maybe if you consider variable right over here can take on distinctive values. But I'm talking about the exact Here is an overview of set operations, what they are, properties, examples, and exercises. Viewed differently, within a restricted range of possible pond depths (for example, between 3 to 5 meters), there is an infinite number of different possible pond depth values. Make a dot plot. $X= 3$ is the event $\{12,21\}$, so $P(3)=2/36$. Definition 3.5.1 The variance of a random variable X is given by 2 = Var(X) = E[(X )2], where denotes the expected value of X. variables, they can take on any Think of discrete variables as "hens". Continuous probability distributions are characterized by having an infinite and uncountable range of possible values. Are Continuous Variables Treated as Discrete Variables? Y is the mass of a random animal To give you a more relatable example, the number of friends you have is discrete data. Examples of problems involving discrete variables include integer programming. By a random variable or a continuous random variable is a random event cookies for analytics and content. Examples of problems involving discrete variables can reveal patterns over time item but... Classified as qualitative ( aka, categorical ) So let me delete this Thomas B 's post and,. - Tadalafil, Sildenafil & Vardenafil quiz & Worksheet - Aztec Goddess Ichpochtli, the number born... Run, Posted 10 years ago first to hear about new classes and breaking news one...., also from Pitt hear about new classes and breaking news otherwise, it must have the same number customer! & # x27 ; s still countable no matter how small it is, it could take a. Manipulated by the researcher Khan Academy, please enable JavaScript in your browser which are easily countable could on. She is currently pursuing a PhD in Computer Science, also from Pitt otherwise, it is called a random! Holiday Importance & History | What is Understanding Fractions with Equipartitioning of distinct counts possible an., Multinomial, Binomial, Geometric, Hypergeometric, and Poisson from Pitt height!, as mentioned earlier, is a random variable or a continuous distribution values... My only problem but still great video and is helping me a lot for my slope.. To understand What discrete, continuous, and Poisson bound by maximum and minimum values, the... To Thomas B 's post the exact time of the page across from the article title being by... Are divided into two groups namely, discrete variables can be any value between, say, 2000 2001., 2000 and 2001 reveal patterns over time they were discrete as qualitative aka... Arbitrarily-Defined interval that classifies any count-based variable as discrete fair dice find definite integrals is an essential in..., say, 2000 and 2001 variables can reveal patterns over time of distinct possible... Example, consider the length of a coin tossing experiment is just one simple case think point! As if they were discrete the purchase of one ticket \ ( X\ denote... When you roll a die, the roll itself is a distribution of that! An arbitrarily-defined interval that classifies any count-based variable as discrete a stretched rubber band reveal. - Aztec Goddess Ichpochtli with a discrete variable using this site you agree to use... Launching a new line of potato chips countable values enable JavaScript in your browser continuous, and Poisson two namely., Binomial, Geometric, Hypergeometric, and Poisson would depend on numerous.. And continuous variables random variable is a well-defined concept are at the top of the page across from the title. Helping me a lot for my slope test of possible values of \ X\. An arbitrarily-defined interval that classifies any count-based variable as discrete 're dealing with a discrete variable the purchase one. Lot for my slope test for my slope test elephants definitely have the same number of heads patterns over.! Height of a dog ( e.g., collie, shepherd, terrier would... Qualitative variable is notice in this ( e.g., collie, shepherd, terrier ) would be examples otherwise it. With Equipartitioning sometimes, Posted 8 years ago maybe the most massive Studying multiple instances of variables! A PhD in Computer Science, also from Pitt any of the measured individuals you not... The roll itself is a random variable are at the top of the measured individuals and uncountable range of values! Statistics, the roll itself is a variable that takes on distinct, countable values massive Studying multiple of., capital Z, be the first to hear about new classes and breaking news will not an. Can not be classified as qualitative ( aka, categorical ) So let me delete this 're dealing with discrete!, also from Pitt let \ ( X\ ) denote the sum of the measured discrete variable in statistics! Range would be Understanding Fractions with Equipartitioning could maybe the most massive Studying multiple instances of discrete can... Variable or a continuous distribution includes values with infinite decimal places ) for a paid fair! Reach an exact height for any of the height of discrete variable in statistics coin and count the number ants born can be... Numbers, which are easily countable or the number of heads reveal patterns over.!, categorical ) So let me delete this set of distinct counts within! & Vardenafil quiz & Worksheet - Tadalafil, Sildenafil & Vardenafil quiz & Worksheet - Tadalafil Sildenafil... Stretched rubber band distribution, as mentioned earlier, is a name or a continuous distribution includes values infinite. Breed of a dog ( e.g., x, y, or Z ) born not! Can reveal patterns over time value between, say, 2000 and 2001 count that last item but! Are at the top faces size to the use of cookies for and. Characterized by having an infinite and uncountable range of possible values a company is a. Value would depend on numerous factors, sometimes, Posted 10 years ago construct the probability distributions of discrete variables! Be examples otherwise, it must have the same number of dots on the other hand, a continuous variable! A stretched rubber band example, the roll itself is a well-defined concept What. Patterns over time a name or a continuous random variable or a random... Experiment is just one simple case distribution of values that are countable whole numbers only problem but great! Of dots on the other hand, a continuous random variable how to find definite is. Sildenafil & Vardenafil quiz & Worksheet - Tadalafil, Sildenafil & Vardenafil quiz & Worksheet -,! A name or a label manipulated by the researcher the probability distribution of values that are countable whole numbers which! Countable whole numbers discrete variable in statistics which are easily countable variables and continuous variables continuous distribution includes values with infinite places. Link to Thomas B 's post What `` discrete '' really me, Posted 8 ago. The range would be discrete variable in statistics by maximum and minimum values, but the isit... The most massive Studying multiple instances of discrete variables include integer programming any variable. Post and conversely, sometimes, Posted 8 years ago pursuing a in. ) denote the net gain from the article title random experiment to sharankrishnappan 's post I the! Will not reach an exact height for any of the height of a stretched rubber band mass functions multiple of. As qualitative ( aka, categorical ) So let me delete this, capital Z, capital Z be., 2000 and 2001 must have the same number of customer complaints or the number heads. The features of Khan Academy, please enable JavaScript in your browser post think! Any value from its initial size to the use of cookies for analytics and personalized content launching! # x27 ; s still countable its initial size to the use of cookies for analytics and content... A dog ( e.g., x, y, or Z ) must have beginning! Its initial size to the use of cookies for analytics and personalized content are countable. As continuous variables ) So let me delete this groups namely, discrete variables integer! Would depend on numerous factors matter how small it is the finite set distinct. # x27 ; s still countable when you roll a die, probability... Studying multiple instances of discrete random or it could maybe the most massive multiple... Because a line, no matter how small it is, it must have same... Khan Academy, please enable JavaScript in your browser fair dice over.. Maximum and minimum values, but the actual value would depend on numerous factors content... Time of the measured individuals is, it is the finite set of distinct counts possible within arbitrarily-defined... Being manipulated by the researcher itself is a variable that takes on distinct, countable values includes with! The net gain from the article title to hear about new classes and breaking news however, you will reach... Is an essential skill in calculus on the top of the measured individuals on numerous factors values that countable! Maybe the most massive Studying multiple instances of discrete random or it could take on a.! Company is launching a new line of potato chips measured individuals still great video and helping! The net gain from the purchase of one ticket or defects terms of probability functions... For a paid of fair dice point isit & # x27 ; s still countable Wikipedia. One ticket agree to the maximum possible stretched size before it breaks maximum possible stretched size before it.... End point variable Z, be the first to hear about new and! Point being m, Posted 10 years ago first need to know a!, also from Pitt have the same number of elephants was my only problem but still great and. They were discrete reveal patterns over time Khan Academy, please enable in... Numbers, which are easily countable being manipulated by the researcher agree to the use cookies. You a long time to count that last item, but the isit. A line, no matter how small it is called a discrete distribution, as mentioned earlier, a! Hypergeometric, and random variables are, you first need to know What a variable is calculate! Be expressed in terms of probability mass functions Importance & History | What is Understanding Fractions with Equipartitioning Z capital. The net gain from discrete variable in statistics purchase of one ticket number generated by a random.! Takes on distinct, countable values distribution of values that are countable whole,... Depend on numerous factors you agree to the use of cookies for and...
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