Answered: (b) Give E(X) and Var(X). (c) Give E(X…

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Probability

(b) Give E(X) and Var(X). (c) Give E(X | Y = 2) and Var(X | Y = 2).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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I need help with this parts b and c please

A convenience store has two separate locations where customers can be checked out as they leave. These locations each have two cash registers and two employees who check out customers. Let X be the number of cash registers being used at a particular time for location 1 and Y the number being used at the same time for location 2. The joint probability function is given by the accompanying table. Complete parts (a) through (c) below.

Joint Probability Function
X
0
1
2
0
0.13
0.06
0.07
y
1
0.04
0.24
0.13
2
0.04
0.03
0.26

(a) Give the marginal density of both X and Y as well
as the probability distribution of X given Y = 2.
(b) Give E(X) and Var(X).
(c) Give E(X | Y = 2) and Var(X | Y = 2).

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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Step 1: Expectation of Random variables

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