Question

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.

P(x,y)	y
x		0	1	2
	0	0.06	0.14	0.02
	1	0.03	a	0.1
	2	0.06	0.08	0.19

e.) What is E(Y|X=0)?

f.) What is Var(Y|X=0)?

l.) Standard deviation of X?

m.) Standard deviation of Y?

n.) Corr(X,Y)?

Answer 1