Random Variable

Thirteen cards are drawn without replacement from a standard bridge deck. Let X1,X2,...,X13 denote the numbers of points assigned to the cards drawn.

Ace=Point 4.
King=Point 3.
Queen=Point 2.
Jack=Point 1.
Otherwise=Point 0.

(a) Find E(Xi) and Var(Xi) for i=1,2,...,13
(b)(i) Find the expected total number of points obtained.
(ii) Is it true that Var(X1+X2+...+X13)=Var(X1)+Var(X2)+...+Var(X13)?