Question

An Outlet runs a promotion. All customers who visit the store on Sunday will receive a gift certificate worth a random amount that is Discrete Uniform on {$11,..,$20}. The managers expect the number of customers to visit the store during the promotion and receive a gift certificate is Discrete Uniform on {51..,100}. What are the expected value and variance of total payouts on the promotional gift certificates?

Answer 1

Mean = $ 1170.25

Variance = 98777.1875

Let X be the random nariable for getto and Y be the random nariable for number of customers and be the random nariable for total payout Z = XY Mean total payout = E(2) E (2) = EXY) = Ex(x). Ey (Y) - 11+20 x 514100 = 15.5x 7505 = $ 1170-25 Var (XY)= (ort light leg) - urdu For unosom distrilestion 12 ² (l-QH)²) a= leta . Var(y) = 5(20-11+12, "72-6+ 2041037 {(10-51933-72100 4322 F - (20+11,2 (10075172 - (8.257240125) (208-25+5700.25) - 240-25x5700.25 = 248-5x5908-5 - 240.25 +5700.25 = 1468262.25 - 1369485.0625 98777-1875 - Variance 98747.18 Ano- Mean $ 1170.25 variance 98777-18