Table of Contents

## How do you find the mean of a discrete random variable?

The mean μ of a discrete random variable X is a number that indicates the average value of X over numerous trials of the experiment. It is computed using the formula μ=∑xP(x).

## What is the variance of the random variable?

In words, the variance of a random variable is the average of the squared deviations of the random variable from its mean (expected value). Notice that the variance of a random variable will result in a number with units squared, but the standard deviation will have the same units as the random variable.

## What does discrete mean in discrete random variables?

A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,…….. Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete.

## How do you find the mean variance and standard deviation of a discrete probability distribution?

To find the variance σ2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products. To find the standard deviation σ of a probability distribution, simply take the square root of variance σ2.

## What formula is used to find the variance of discrete random variable?

For a discrete random variable X, the variance of X is obtained as follows: var(X)=∑(x−μ)2pX(x), where the sum is taken over all values of x for which pX(x)>0. So the variance of X is the weighted average of the squared deviations from the mean μ, where the weights are given by the probability function pX(x) of X.

## How do you find the variance of two random variables?

One of the applications of covariance is finding the variance of a sum of several random variables. In particular, if Z=X+Y, then Var(Z)=Cov(Z,Z)=Cov(X+Y,X+Y)=Cov(X,X)+Cov(X,Y)+Cov(Y,X)+Cov(Y,Y)=Var(X)+Var(Y)+2Cov(X,Y).

## How do you calculate the variance of a random variable?

For a discrete random variable the variance is calculated by summing the product of the square of the difference between the value of the random variable and the expected value, and the associated probability of the value of the random variable, taken over all of the values of the random variable. In symbols, Var(X) = (x – µ) 2 P(X = x)

## What is the expected value for a random variable?

Definition (informal) The expected value of a random variable is the weighted average of the values that can take on, where each possible value is weighted by its respective probability.

## What is the formula for a random variable?

1. If X is a random variable, then V(aX+b) = a2V(X), where a and b are constants.

## What is the standard deviation of a random variable?

Standard deviation (of a discrete random variable) A measure of spread for a distribution of a random variable that determines the degree to which the values differ from the expected value. The standard deviation of random variable X is often written as σ or σX.