Answered: Let X be the number of bathrooms in a…

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

Let X be the number of bathrooms in a randomly selected house for sale in Malibu, California. Suppose X has the following probability distribution, where p(x) is the probability mass function, and F(x) is the cumulative distribution function.

x	1	2	3	4	5	6
p(x)	.05	.20	.32	.27	.10	.06
F(x)	.05	.25	.57	a	.94	1

a. What is the value of a?
b. Calculate the probability that X < 3.
c. Calculate the expected value of X.
d. Calculate the variance of X.
e. Calculate the expected value of

x^0.37

<_>
f. We randomly and independently select 3 different houses for sale in Malibu. What is the probability that each of the 3 selected houses has exactly 3 bathrooms?
g. We randomly and independently select 3 different houses for sale in Malibu. What is the probability that exactly two of the selected houses have exactly 2 bathrooms ?
h. Malibu has a water crisis. The town board will solve this crisis by charging a special water tax. This tax will equal $131 multiplied by the number of bathrooms. What is the expected total tax revenue for 15000 randomly selected Malibu homes?
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