Find the mean and variance of $X$. 2. Then the random variable $X$ take the values $X=1,2,3,4,5,6$ and $X$ follows $U(1,6)$ distribution. The variance of discrete uniform distribution $X$ is, \begin{aligned} V(X) &=\frac{(6-1+1)^2-1}{12}\\ &=\frac{35}{12}\\ &= 2.9167 \end{aligned}, A telephone number is selected at random from a directory. In general, PX()=x=px(), and p can often be written as a formula. For variance, we need to calculate $E(X^2)$. Let $X$ denote the number appear on the top of a die. This geometric probability calculator is used to find geometric distribution probability with total number of occurrence & probability … Â© VrcAcademy - 2020About Us | Our Team | Privacy Policy | Terms of Use. a. Let the random variable $X$ have a discrete uniform distribution on the integers $9\leq x\leq 11$. The probability that the last digit of the selected number is 6, \begin{aligned} P(X=6) &=\frac{1}{10}\\ &= 0.1 \end{aligned}, b. \end{aligned} $$, And variance of discrete uniform distribution Y is,$$ \begin{aligned} V(Y) &=V(20X)\\ &=20^2\times V(X)\\ &=20^2 \times 2.92\\ &=1168. Then the mean of discrete uniform distribution $Y$ is, \begin{aligned} E(Y) &=E(20X)\\ &=20\times E(X)\\ &=20 \times 2.5\\ &=50. If you continue without changing your settings, we'll assume that you are happy to receive all cookies on the vrcacademy.com website. If we consider to be a random variable that takes the values then the uniform distribution would assign each value a probability … \end{aligned}. b. The mean μ of a discrete random variable X is a number that indicates the … Geometric Distribution Uniform (Discrete) Distribution. The probability mass function (pmf) of random variable $X$ is, \begin{aligned} P(X=x)&=\frac{1}{6-1+1}\\ &=\frac{1}{6}, \; x=1,2,\cdots, 6. 1. 6. Discrete uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter a and b. Suppose X denote the number appear on the top of a die. The probability that the number appear on the top of the die is less than 3 is, \begin{aligned} P(X < 3) &=P(X=1)+P(X=2)\\ &=\frac{1}{6}+\frac{1}{6}\\ &=\frac{2}{6}\\ &= 0.3333 \end{aligned} $$The probability distribution of a discrete random variable X is a listing of each possible value x taken by X along with the probability P(x) that X takes that value in one trial of the experiment. The probability mass function (pmf) of X is,$$ \begin{aligned} P(X=x) &=\frac{1}{11-9+1} \\ &= \frac{1}{3}; x=9,10,11. Let the random variable $X$ have a discrete uniform distribution on the integers $0\leq x\leq 5$. The probability mass function (pmf) of $X$ is, \begin{aligned} P(X=x) &=\frac{1}{5-0+1} \\ &= \frac{1}{6}; x=0,1,2,3,4,5. Discrete uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter a and b. To analyze our traffic, we use basic Google Analytics implementation with anonymized data. c. Compute mean and variance of X. \end{aligned}, The variance of discrete uniform distribution $X$ is, \begin{aligned} V(X) &=\frac{(8-4+1)^2-1}{12}\\ &=\frac{25-1}{12}\\ &= 2 \end{aligned}, c. The probability that $X$ is less than or equal to 6 is, \begin{aligned} P(X \leq 6) &=P(X=4) + P(X=5) + P(X=6)\\ &=\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\\ &= \frac{3}{5}\\ &= 0.6 \end{aligned}. The probability that the last digit of the selected telecphone number is less than 3, \begin{aligned} P(X < 3) &=P(X\leq 2)\\ &=P(X=0) + P(X=1) + P(X=2)\\ &=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\\ &= 0.1+0.1+0.1\\ &= 0.3 \end{aligned}, c. The probability that the last digit of the selected telecphone number is greater than or equal to 8, \begin{aligned} P(X\geq 8) &=P(X=8) + P(X=9)\\ &=\frac{1}{10}+\frac{1}{10}\\ &= 0.1+0.1\\ &= 0.2 \end{aligned}. The probability distribution is often denoted by pm(). Code to add this calci to your website Discrete Random Variable's expected value,variance and standard deviation are calculated easily. 4 of theese distributions are available here. The Discrete uniform distribution, as the name says is a simple discrete probability distribution that assigns equal or uniform probabilities to all values that the random variable can take. This list has either a finite number of members, or at most is countable. The possible values of $X$ are $0,1,2,\cdots, 9$. You can refer below recommended articles for discrete uniform distribution theory with step by step guide on mean of discrete uniform distribution,discrete uniform distribution variance proof. Copyright (c) 2006-2016 SolveMyMath. Find the probability that an even number appear on the top, 1. \end{aligned} $$, Now, Variance of discrete uniform distribution X is,$$ \begin{aligned} V(X) &= E(X^2)-[E(X)]^2\\ &=100.67-[10]^2\\ &=100.67-100\\ &=0.67. \end{aligned} , eval(ez_write_tag([[250,250],'vrcacademy_com-banner-1','ezslot_9',127,'0','0']));a. Determine mean and variance of Y. \end{aligned}. Chapter 4 Discrete Probability Distributions 93 This gives the probability distribution of M as it shows how the total probability of 1 is distributed over the possible values. A discrete random variable $X$ is said to have uniform distribution with parameter $a$ and $b$ if its probability mass function (pmf) is given byeval(ez_write_tag([[580,400],'vrcacademy_com-medrectangle-3','ezslot_4',126,'0','0'])); $$f(x; a,b) = \frac{1}{b-a+1}; x=a,a+1,a+2, \cdots, b$$, $$P(X\leq x) = F(x) = \frac{x-a+1}{b-a+1}; a\leq x\leq b$$, The expected value of discrete uniform random variable $X$ is, The variance of discrete uniform random variable $X$ is, A general discrete uniform distribution has a probability mass function, Distribution function of general discrete uniform random variable $X$ is, The expected value of above discrete uniform random variable $X$ is, The variance of above discrete uniform random variable $X$ is. \end{aligned} $$, Mean of discrete uniform distribution X is,$$ \begin{aligned} E(X) &=\sum_{x=9}^{11}x \times P(X=x)\\ &= \sum_{x=9}^{11}x \times\frac{1}{3}\\ &=9\times \frac{1}{3}+10\times \frac{1}{3}+11\times \frac{1}{3}\\ &= \frac{9+10+11}{3}\\ &=\frac{30}{3}\\ &=10. Thus the random variable $X$ follows a discrete uniform distribution $U(0,9)$. The probability that an even number appear on the top of the die is, \begin{aligned} P(X=\text{ even number }) &=P(X=2)+P(X=4)+P(X=6)\\ &=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\\ &=\frac{3}{6}\\ &= 0.5 \end{aligned} Suppose $X$ denote the last digit of selected telephone number. 3. \end{aligned} $$,$$ \begin{aligned} E(X^2) &=\sum_{x=0}^{5}x^2 \times P(X=x)\\ &= \sum_{x=0}^{5}x^2 \times\frac{1}{6}\\ &=\frac{1}{6}( 0^2+1^2+\cdots +5^2)\\ &= \frac{55}{6}\\ &=9.17. Determine mean and variance of $X$. \end{aligned} , Let Y=20X. \end{aligned}, \begin{aligned} V(X) &= E(X^2)-[E(X)]^2\\ &=9.17-[2.5]^2\\ &=9.17-6.25\\ &=2.92. Below are the few solved examples on Discrete Uniform Distribution with step by step guide on how to find probability and mean or variance of discrete uniform distribution. Continuous Uniform Distribution Calculator, Weibull Distribution Examples - Step by Step Guide, Karl Pearson coefficient of skewness for grouped data. Let the random variable Y=20X. \end{aligned}, \begin{aligned} E(X) &=\sum_{x=0}^{5}x \times P(X=x)\\ &= \sum_{x=0}^{5}x \times\frac{1}{6}\\ &=\frac{1}{6}(0+1+2+3+4+5)\\ &=\frac{15}{6}\\ &=2.5. Find the probability that the number appear on the top is less than 3. The mean of discrete uniform distribution X is, \begin{aligned} E(X) &=\frac{4+8}{2}\\ &=\frac{12}{2}\\ &= 6. Some Examples include 'chance of three random points on a plane forming an acute triangle', 'calculating mean area of polygonal region formed by random oriented lines over a plane'. Discrete Random Variable Calculator Online probability calculator to find expected value E (x), variance (σ 2) and standard deviation (σ) of discrete random variable from number of outcomes.

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