Chapter 7.2, Problem 21E

A library subscribes to two different weekly news magazines, each of which is supposed to arrive in Wednesday’s mail. However, each one might actually arrive on Wednesday (W), Thursday (T), Friday (F), or Saturday (S). Suppose that the two magazines arrive independently of one another and that for each magazine

$P(\text{W})=0.4,P(\text{T})=0.3,P(\text{F})=0.2,\text{and}(S)=0.1$

Define a random variable y by

$\begin{array}{l}y=\text{the}\text{number}\text{of}\text{days}\text{beyond}\text{Wednesday}\text{that}\text{it}\hfill \\ \text{takes}\text{for}\text{both}\text{magazines}\text{to}\text{arrive}.\hfill \end{array}$

For example, if the first magazine arrives on Friday and the second magazine arrives on Wednesday, then y = 2. If both magazines arrive on Thursday, y = 1. Determine the probability distribution of y. (Hint: Draw a tree diagram with two generations of branches, the first labeled with arrival days for Magazine 1 and the second for Magazine 2.)