Common questions

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. …