2. ÷ --4 points DevoreStat3 3.E.0 19. My Notes Ask Your Teacher A library subscr

Question

2. ÷ --4 points DevoreStat3 3.E.0 19. My Notes Ask Your Teacher 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.) = 0.22, p(Thurs.) = 0.34, p(Fri.) = 0.19, and p(Sat.) = 0.25. Let Y= the number of days beyond wednesday that it takes for both magazines to amive (so possible values are 0, 1, 2, or 3). Compute the pmf of y, [Hint: There are 16 possible outcomes; y(W,W)-0, YtF,Th) 2, and so on.] Enter your answers to four decimal places.) Pry)

Explanation / Answer

Here first we take the 16 possible outcomes and their probabilties.

Here, Pr(W) = 0.22, Pr(Th) = 0.34 , Pr(Fr) = 0.19 and Pr(Sat) = 0.25

So, Here

P(Y ) = 0.0484, Y = 0

= 0.0748 + 0.0748 + 0.1156 = 0.2652 ; Y = 1

= 0.0418 + 0.0646 + 0.0418 + 0.0646 + 0.0361 = 0.2489 ; Y = 2

= 0.055 + 0.085 + 0.0475 + 0.055 + 0.085 + 0.0475 + 0.0625 = 0.4375 ; Y = 3

The bold values are answer here.

Possiblities Magzine 1 Pr(X1) Magzine 2 Pr(X2) Y value Pr(Y) = Pr(X1) * Pr(X2) 1 W 0.22 W 0.22 0 0.0484 2 W 0.22 Th 0.34 1 0.0748 3 W 0.22 Fr 0.19 2 0.0418 4 W 0.22 Sat 0.25 3 0.055 5 Th 0.34 W 0.22 1 0.0748 6 Th 0.34 Th 0.34 1 0.1156 7 Th 0.34 Fr 0.19 2 0.0646 8 Th 0.34 Sat 0.25 3 0.085 9 Fr 0.19 W 0.22 2 0.0418 10 Fr 0.19 Th 0.34 2 0.0646 11 Fr 0.19 Fr 0.19 2 0.0361 12 Fr 0.19 Sat 0.25 3 0.0475 13 Sat 0.25 W 0.22 3 0.055 14 Sat 0.25 Th 0.34 3 0.085 15 Sat 0.25 Fr 0.19 3 0.0475 16 Sat 0.25 Sat 0.25 3 0.0625

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