The amount of money Joey takes with him to the floating casino is a random variable Z (in thousands) described by the pdf J5: 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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The amount of money Joey takes with him to the floating casino is a random variable Z (in thousands)
described by the pdf
*: 0 < x < 6
| 0, otherwise
18
f(r) =
He has a lot of experience in gambling. Decades of experience have shown that over the course of an
evening, he never wins. In fact, the conditional pdf of the amount of money with which he returns home
on any particular night given that his original wealth is X = x is uniformly distributed between 0 and x.
a. Find f(y), the marginal pdf of the amount he will bring home on a randomly selected night.
b. Determine the expected value of his loss on any particular night.
c. Find the conditional probability that he started out for the casino with less than 2000 pesos given
that he returned home with less than 2000 pesos.
Transcribed Image Text:The amount of money Joey takes with him to the floating casino is a random variable Z (in thousands) described by the pdf *: 0 < x < 6 | 0, otherwise 18 f(r) = He has a lot of experience in gambling. Decades of experience have shown that over the course of an evening, he never wins. In fact, the conditional pdf of the amount of money with which he returns home on any particular night given that his original wealth is X = x is uniformly distributed between 0 and x. a. Find f(y), the marginal pdf of the amount he will bring home on a randomly selected night. b. Determine the expected value of his loss on any particular night. c. Find the conditional probability that he started out for the casino with less than 2000 pesos given that he returned home with less than 2000 pesos.
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