Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y), y = 1, 3, 5. c. List the cumulative distribution function F(x)

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

Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below:
a. Find the marginal distribution g(x), x = 1, 2, 3.
b. Find the marginal distribution h(y), y = 1, 3, 5.
c. List the cumulative distribution function F(x).
d. List the cumulative distribution function F(y).
e. Find the conditional distribution of f (x|y), P(X = 1 | Y = 3).
f. Find the conditional distribution of f (y|x), P(X = 3 | Y = 3).
g. Determine if the random variables are statistically independent considering f (2, 1).

f(x,y)
1
3
У
сл со
5
1
0.05
0.05
0.00
x
2
0.05
0.10
0.20
3
0.10
0.35
0.10

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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