The central limit theorem and the standard error of the mean σ ( X ) = σ ( X ) are n based on the premise that the population has infinitely many members. When samples are chosen with replacement the population is effectively infinite. Consider the population of N= 5 objects {1, 2, 3, 4, 5}. 1. Find the population mean μ 2. Find the population std. deviation σ 3. Take (with replacement) samples of size n=2 from the above population. (1,1) (1,2) (1,3) (1,4) (1,5) (2,1) (2,2) a. How many such samples are possible?b. List all the X ’s, i. e. the means of all these samples of size 2 c. Find the mean of these means, i. e. E(X) d. Is E(X)=μ? e. Find the standard errorσ(X), i. e. the std. deviation of all these means σ(X)f. Show that the standard error equals