1 Let X1 and X2 be independent random variables Suppose the

1). Let X1 and X2 be independent random variables. Suppose the mean and variance of X1 are 2 and 4, respectively. Suppose, the mean and variance of X2 are 3 and 5 respectively.

What is the mean and variance of X1 + X2 ?

2). Suppose, X1 X2 X 3 X 4 X5 are a random sample of size 5 from any distribution.

1. Find the sample mean ( that is find X bar)?

2. After finding the sample mean (X Bar) then find the expected value of X bar (e.g. E(X bar))? 3. Also find the variance of X bar (e. g. V(X bar)

Solution

Mean of the Sum of Two Random Variables: If X and Y are random variables, then