Answered: Given the probability distributions…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Given the probability distributions shown below, complete the following parts.

a. Compute the expected value for each distribution A and B.

b. Compute the standard deviation for each distribution.

c. What is the probability that x will be at least 3 in Distribution A and Distribution B?

d. Compare the results of distributions A and B.

Distribution A: xi	Distribution A: P(X=xi)	Distribution B: xi	Distribution B: P(X=xi)
0	0.51	0	0.04
1	0.2	1	0.09
2	0.16	2	0.16
3	0.09	3	0.2
4	0.04	4	0.51

Expert Solution

Step 1: Part a

Since you have posted a question with multiple subparts, we will provide solution to the first three sub-parts as per our Q&A guidelines. Please repost the remaining sub parts separately.

For distribution A:

Expected value E(X) = $sum from blank to blank of x. P left parenthesis X equals x right parenthesis equals 0 asterisk times 0.51 plus 1 asterisk times 0.2 plus 2 asterisk times 0.16 plus 3 asterisk times 0.09 plus 4 asterisk times 0.04 equals 0.95$

For distribution B:

Expected value E(X) = $sum from blank to blank of x. P left parenthesis X equals x right parenthesis equals 0 asterisk times 0.04 plus 1 asterisk times 0.09 plus 2 asterisk times 0.16 plus 3 asterisk times 0.2 plus 4 asterisk times 0.51 equals 3.05$