A library subscribes to two different weekly news magazines

A library subscribes to two different weekly news magazines, each of which is supposed to arrive in Wednesday’s mail. In actuality, each may arrive on Wednesday, Thursday, Friday, or Saturday. Suppose the two arrive independently of each other, and for each one P(Wednesday arrival) = 0.3, P(Thursday arrival) = 0.4, P(Friday arrival) = 0.2 and P(Saturday arrival) = 0.1. Let Y = number of days beyond Wednesday it takes for both magazines to arrive. Find the pmf of Y.

Solution

We let Y = 0 to be wednesday. Hence,

P(Y) = 0.3, Y = 0
0.4, Y = 1
0.2, Y = 2
0.1, Y = 3