# How do you find the variance of an independent random variable?

## How do you find the variance of an independent random variable?

For independent random variables X and Y, the variance of their sum or difference is the sum of their variances: Variances are added for both the sum and difference of two independent random variables because the variation in each variable contributes to the variation in each case.

**What are some real life situations that can be represented as random variables?**

A typical example of a random variable is the outcome of a coin toss. Consider a probability distribution in which the outcomes of a random event are not equally likely to happen. If random variable, Y, is the number of heads we get from tossing two coins, then Y could be 0, 1, or 2.

**How do you prove variance?**

Here is a useful formula for computing the variance. To prove it note that Var(X)=E[(X−μX)2]=E[X2−2μXX+μ2X]=E[X2]−2E[μXX]+E[μ2X] by linearity of expectation.

### How do you find the variance of a 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.

**What is a real life example of a variable?**

A variable is a number that does not have a fixed value. The picture and the list below show some real-life examples, where the value of a variable changes with the change in place and time. The temperature in different places also change. The height of a growing child changes with time.

**What does a variance of 0 mean?**

A large variance indicates that numbers in the set are far from the mean and far from each other. A variance value of zero, though, indicates that all values within a set of numbers are identical. Every variance that isn’t zero is a positive number. A variance cannot be negative.

#### What is variance of a variable?

A measure of spread for a distribution of a random variable that determines the degree to which the values of a random variable differ from the expected value. The square root of the variance is equal to the standard deviation. …