Question

peldataka SMBSCONEGLOSBEXAM. XOGOM Asignación # 12 Distribución de Probabilidad Discreta, Media y Desviación Estándar (4.3.4.4) Page 12 of 12 Scoate Ask Myne Des NE Sabila F50142Exp6 Esemeteater the Weight: Back Delete Clear Kristine purchased a 550 ticket from a private lottery. The rules of the game were as follows: She would win a $1000 with a 1 in 1600 chance, $500 with a 1 in a 1000 chance, S300 with a 1 in 500 chance and S50 with a 1 in 200 chance. Otherwise she would lose the original S50 investment. Find the expected value and standard deviation of this game. Graph the distribution (Round the answer up to 2 decimal places) Click here to enter answer E the we Expected value Standard Deviation Select the Done Copyright 2005 - 2019 daca ne 9

Answer 1

Let random variable X denote the payoff = winning amount - ticket price

If she wins $1000, payoff X = 1000-50 = 950, P(950) = 1/1600 = 0.000625

If she wins $500, X = 500-50 = 450, P(450) = 1/1000 = 0.001

If she wins $300, X =300-50 = 250, P(250) = 1/500 = 0.002

If she wins $50, X =50-50 = 0, P(0) = 1/200 = 0.005

If she wins nothing, X = 0-50= -50, P(-50) = 1 - 1/1600 - 1/1000 - 1/500 - 1/200 = 0.991375

Expected value E(X) = $\sum x.P(X)$ = -42.6813

Standard deviation $\sigma$ = $\sqrt{\sum (X - \bar X)^2P(X)}$ = 32.61287

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