Need help with this Intro to probability and statistics homework problem. Below the homework problem is the answers from the textbook. Make sure your handwriting is neat and readable. 3.2-13. If X is x²(23), find the following:(a) P(14.85 < X < 32.01).(b) Constants a and b such that P(a < X < b) = 0.95 andP(X < a) = 0.025.(c) The mean and variance of X.(d) xos (23) and X95 (23). 3.2-13 (a) 0.80; (b) a = 11.69, b = 38.08; (c) μ = 23,0²46; (d) 35.17, 13.09.

Answered: 3.2-13. If X is x (23), find the…

3.2-13. If X is x (23), find the following: (a) P(14.85 < X < 32.01). (b) Constants a and b such that P(a < X < b) = 0.95 and P(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

Need help with this Intro to probability and statistics homework problem. Below the homework problem is the answers from the textbook. Make sure your handwriting is neat and readable.

3.2-13. If X is x²(23), find the following:
(a) P(14.85 < X < 32.01).
(b) Constants a and b such that P(a < X < b) = 0.95 and
P(X < a) = 0.025.
(c) The mean and variance of X.
(d) xos (23) and X95 (23).

3.2-13 (a) 0.80; (b) a = 11.69, b = 38.08; (c) μ = 23,0²
46; (d) 35.17, 13.09.

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Expert Solution

Step 1

A chi square distribution is a right tailed distribution. It is the distribution of sum of the squares of independent standard normal random variates with $n$ as the degree of freedom.

The mean and the variance for ${χ^{2}}_{(n)}$ can be obtained using the formulae:

$μ = d f$

$σ^{2} = 2 \times d f$

Here, $df$ is the degree of freedom, $μ$ is the mean of the distribution and $σ^{2}$ is the variance of the distribution.

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