Question

The variance of the sum of two independent random variables is the sum of the variances of each random variable.

a. True
b. False

Answer 1

False - the variance of the sum of two independent random variables is not the sum of the variances of each random variable, but equal to the sum of the variances plus twice the covariance between the variables.

Step-by-step explanation:

False - the variance of the sum of two independent random variables is not the sum of the variances of each random variable. In fact, the variance of the sum of two independent random variables is equal to the sum of the variances of each random variable plus twice the covariance between the two variables. This can be mathematically represented as:

Var(X + Y) = Var(X) + Var(Y) + 2Cov(X, Y)

where Var(X) and Var(Y) are the variances of X and Y, and Cov(X, Y) is the covariance between X and Y.