discrete probability distribution calculator

Let the random variable $X$ have a discrete uniform distribution on the integers $0\leq x\leq 5$. Determine mean and variance of $Y$. The probability mass function (pmf) of $X$ is, $$ \begin{aligned} P(X=x) &=\frac{1}{5-0+1} \\ &= \frac{1}{6}; x=0,1,2,3,4,5. Hope you like article on Discrete Uniform Distribution. Suppose $X$ denote the number appear on the top of a die. The probability that the last digit of the selected number is 6, $$ \begin{aligned} P(X=6) &=\frac{1}{10}\\ &= 0.1 \end{aligned} $$, b. \end{aligned} $$. The probability that the number appear on the top of the die is less than 3 is, $$ \begin{aligned} P(X < 3) &=P(X=1)+P(X=2)\\ &=\frac{1}{6}+\frac{1}{6}\\ &=\frac{2}{6}\\ &= 0.3333 \end{aligned} $$ Find the mean and variance of $X$. © VrcAcademy - 2020About Us | Our Team | Privacy Policy | Terms of Use. 4 of theese distributions are available here. 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. b. Calculator of Mean And Standard Deviation for a Probability Distribution Instructions: You can use step-by-step calculator to get the mean (\mu) (μ) and standard deviation (\sigma) (σ) associated to a discrete probability distribution. 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, $$ \begin{aligned} P(X\geq 8) &=P(X=8) + P(X=9)\\ &=\frac{1}{10}+\frac{1}{10}\\ &= 0.1+0.1\\ &= 0.2 \end{aligned} $$. Let $X$ denote the number appear on the top of a die. Find the value of $k$. Discrete Probability Distributions which contains calculators for the most important discrete distributions in mathematics. \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. For variance, we need to calculate $E(X^2)$. c. Compute mean and variance of $X$. Discrete uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter a and b. Geometric Distribution Discrete uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter $a$ and $b$. 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'. \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. b. 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. Suppose $X$ denote the last digit of selected telephone number. 2. Code to add this calci to your website Discrete Random Variable's expected value,variance and standard deviation are calculated easily. \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} $$. Let the random variable $Y=20X$. $P(X=x)=k$ for $x=4,5,6,7,8$, where $k$ is constant. This geometric probability calculator is used to find geometric distribution probability with total number of occurrence & probability … Determine mean and variance of $X$. The probability distribution is often denoted by pm(). The calculator can also solve for the number of trials required. \end{aligned} $$, Mean of discrete uniform distribution $X$ is, $$ \begin{aligned} E(X) &=\sum_{x=9}^{11}x \times P(X=x)\\ &= \sum_{x=9}^{11}x \times\frac{1}{3}\\ &=9\times \frac{1}{3}+10\times \frac{1}{3}+11\times \frac{1}{3}\\ &= \frac{9+10+11}{3}\\ &=\frac{30}{3}\\ &=10. Then the random variable $X$ take the values $X=1,2,3,4,5,6$ and $X$ follows $U(1,6)$ distribution. The mean of discrete uniform distribution $X$ is, $$ \begin{aligned} E(X) &=\frac{4+8}{2}\\ &=\frac{12}{2}\\ &= 6. Roll a six faced fair die. This list has either a finite number of members, or at most is countable. 3. Then the mean of discrete uniform distribution $Y$ is, $$ \begin{aligned} E(Y) &=E(20X)\\ &=20\times E(X)\\ &=20 \times 2.5\\ &=50. \end{aligned} $$, eval(ez_write_tag([[250,250],'vrcacademy_com-banner-1','ezslot_9',127,'0','0']));a. which is the probability mass function (pmf) of discrete uniform distribution. 4. Find the probability that the last digit of the selected number is, eval(ez_write_tag([[728,90],'vrcacademy_com-large-mobile-banner-2','ezslot_13',121,'0','0']));a. 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. Copyright (c) 2006-2016 SolveMyMath. A random variable $X$ has a probability mass function Uniform (Discrete) Distribution. If you continue without changing your settings, we'll assume that you are happy to receive all cookies on the vrcacademy.com website. In general, PX()=x=px(), and p can often be written as a formula. All the numbers $0,1,2,\cdots, 9$ are equally likely. c. The mean of discrete uniform distribution $X$ is, $$ \begin{aligned} E(X) &=\frac{1+6}{2}\\ &=\frac{7}{2}\\ &= 3.5 \end{aligned} $$ 1. 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. The probability mass function (pmf) of random variable $X$ is, $$ \begin{aligned} P(X=x)&=\frac{1}{6-1+1}\\ &=\frac{1}{6}, \; x=1,2,\cdots, 6. \end{aligned} $$. The mean μ of a discrete random variable X is a number that indicates the … \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. All rights are reserved. To understand more about how we use cookies, or for information on how to change your cookie settings, please see our Privacy Policy. Continuous Uniform Distribution Calculator, Weibull Distribution Examples - Step by Step Guide, Karl Pearson coefficient of skewness for grouped data.

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