Suppose that fans will arrive to Kentucky - U Conn final four game according to random variable W = 3X + 2Y + Z. X represents the arrival of fans from the University of Kentucky, which take place according to the exponential distribution with arrival rate of 50 fans per minute. Y represents the arrival of fans from University of Connecticut that is normally distributed N (55, 10) fans per minutes. Z represents independent fans which arrive according to continuous uniform distribution with the parameters (40, 60) fans per minute.
(a) Determine E(W)
(b) Determine V(W)