An urn contains 90 marbles, of which there are 20 green,

20 black and 50 red marbles.

(1) Tom draw marbles without replacement until the 6th green marble. Let X = #

of marbles drawn. Example : GGGBRBGGBRG with x = 11.

(a) What is the value of P(X = 18) ?

(b) What are the numerical values for E(X) and V ar(X) ?

(2) Tom draws 10 marbles without replacement, and Jerry draws 10 marbles without

replacement. Let Y = # of green marbles Tom gets, and Z = # of green marbles Jerry

gets. What are the numerical values for Corr(Y;Z) and Cov(Y;Z) ?