Assignment 04 - Chapter 03 - SOLUTION(1).pdf

# Assignment 04 - Chapter 03 - SOLUTION(1).pdf - ASSIGNMENT 4...

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ASSIGNMENT 4 Question 01 A salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability 0.28, and his second will lead independently to a sale with probability 0.72. Any sale made is equally likely to be either for the deluxe model, which costs \$1,500, or the standard model, which costs \$700. Let X be a random variable that represent the total dollar value of all sales, determine the probability distribution of X. Solution: Let 𝑆 1 , 𝑆 2 = ?ℎ? ????? ?ℎ?? ?ℎ? ????? ???? ??? ?????? ???? ???? ?????????, ???????????? Let 𝑆 1 ̅ , 𝑆 2 ̅̅̅ = ?ℎ? ????? ?ℎ?? ?ℎ? ????? ???? ??? ?????? ???? ???? ??????, ???????????? So we have: 𝑃(𝑆 1 ) = 0.28 ??? 𝑃(𝑆 1 ̅ ) = 0.72 𝑃(𝑆 2 ) = 0.72 ??? 𝑃(𝑆 2 ̅̅̅ ) = 0.28 Let 𝑆𝑀 = ?ℎ? ????? ?ℎ?? ? ????????? ???? ???? ???? ?? ? ???????? ????? Let ?𝑀 = ?ℎ? ????? ?ℎ?? ? ????????? ???? ???? ???? ?? ? ?????? ????? So we have: 𝑃(𝑆𝑀|𝑆 1 ) = 𝑃(𝑆𝑀|𝑆 2 ) = 𝑃(?𝑀|𝑆 1 ) = 𝑃(?𝑀|𝑆 2 ) = 0.5 So if we let X be the total dollar value of all sales, then we notice X will take on the value of 0, 700, 1400, 2200, and 3000 𝑃(0) = 𝑃(𝑆 1 ̅ ∩ 𝑆 2 ̅̅̅ ) = 0.72 ∗ 0.28 = 0.2016 (??????????? ?????) 𝑃(700) = 𝑃(𝑆𝑀|𝑆 1 )𝑃(𝑆 1 )𝑃(𝑆 2 ̅̅̅ ) + 𝑃(𝑆𝑀|𝑆 2 )𝑃(𝑆 2 )𝑃(𝑆 1 ̅ ) = 0.50 ∗ 0.28 ∗ 0.28 + 0.50 ∗ 0.72 ∗ 0.72 = 0.2984 𝑃(1400) = 𝑃(𝑆𝑀|𝑆 1 )𝑃(𝑆 1 )𝑃(𝑆𝑀|𝑆 2 )𝑃(𝑆 2 ) = 0.50 ∗ 0.28 ∗ 0.50 ∗ 0.72 = 0.0504 𝑃(1500) = 𝑃(?𝑀|𝑆 1 )𝑃(𝑆 1 )𝑃(𝑆 2 ̅̅̅ ) + 𝑃(?𝑀|𝑆 2 )𝑃(𝑆 2 )𝑃(𝑆 1 ̅ ) = 0.50 ∗ 0.28 ∗ 0.28 + 0.50 ∗ 0.72 ∗ 0.72 = 0.2984 𝑃(2200) = 𝑃(?𝑀|𝑆 1
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