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. Click the icon to view the joint probability function. (a) Give the marginal density of both X and Y as well as the probability distribution of X given Y = 2. Let g(x) be the marginal density of X and let h(y) be the marginal density of Y. Give the marginal density of both X and Y. X g(x) h(y) 0 1 2 2 (Type integers or decimals. Do not round.)

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. Click the icon to view the joint probability function. (a) Give the marginal density of both X and Y as well as the probability distribution of X given Y = 2. Let g(x) be the marginal density of X and let h(y) be the marginal density of Y. Give the marginal density of both X and Y. X g(x) h(y) 0 1 2 2 (Type integers or decimals. Do not round.)

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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Question

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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.
Click the icon to view the joint probability function.
(a) Give the marginal density of both X and Y as well as the probability distribution of X given Y = 2.
Let g(x) be the marginal density of X and let h(y) be the marginal density of Y. Give the marginal density of both X and
Y.
X
g(x)
y
h(y)
2
0
+8
(Type integers or decimals. Do not round.)
2

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

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Step 2: Find the marginal density of both X and y:

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Step 3: Find the probability distribution of X given Y= 2 is obtained as follows:

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