A library subscribes to two different weekly news magazines, each of which is supposed to arrive in Wednesday's mail. In actuality, each one may arrive on Wednesday, Thursday, Friday, or Saturday. Suppose the two arrive independently of one another, and for each one P(Wed.) = 0.26, P(Thurs.) = 0.34, P(Fri.) = 0.17, and P(Sat.) = 0.23. Let Y = the number of days beyond Wednesday that it takes for both magazines to arrive (so possible Y values are 0, 1, 2, or 3). Compute the pmf of Y. [Hint: There are 16 possible outcomes; Y(W, W) = 0, Y(F, Th) = 2, and so on.] (Enter your answers to four decimal places.)

Step-by-step explanation:

= P (first magazine arrive on wednesday and 2nd magazine arrives on wednesday) = 0.26 x 0.26 = 0.0676

= Probability that one magazine comes on wednesady, the other comes on Thursdays = P( first on WED, 2nd on Thur) or P(2nd on WED, First on THUR) or P(both comes on Thursday)

= 0.26 x 0.34 + 0.34 x 0.26 + 0.34 x 0.34

= 0.2924

= 0.26 x 0.17 + 0.17 x 0.26 + 0.34 x 0.17 + 0.17 x 0.34 + 0.17 x 0.17

= 0.1478

The next part is to find P(Y=3) ; There are seven possibilities here i.e WED and SAT or SAT and WED or THUR and SAT or SAT and THUR or SAT and FRI or FRI and SAT or Both SAT

= 0.26 x 0.23 + 0.23 x 0.26 + 0.34 x 0.23 + 0.23 x 0.34 + 0.17 x 0.23 + 0.23 x 0.17 + 0.23 x 0.23 = 0.3172

the answer is c

step-by-step explanation:

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