A pizza place has two phones. On each phone the waiting time until the first call is exponentially distributed with mean one minute. Each phone is not influenced by the other. Let X be the shorter of the two waiting times and let Y be the longer. It can be shown that the joint pdf of X and Y is f(x,y) = 2e-(a+), 0

A pizza place has two phones. On each phone the waiting time until the first call is exponentially distributed with mean one minute. Each phone is not influenced by the other. Let X be the shorter of the two waiting times and let Y be the longer. It can be shown that the joint pdf of X and Y is f(x,y) = 2e-(a+), 0

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Description: A pizza place has two phones. On each phone thewaiting time until the first call is exponentiallydistributed with mean one minute. Each phone isnot influenced by the other. Let X be the shorter ofthe two waiting times and let Y be the longer.It can

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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A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

A pizza place has two phones. On each phone the
waiting time until the first call is exponentially
distributed with mean one minute. Each phone is
not influenced by the other. Let X be the shorter of
the two waiting times and let Y be the longer.
It can be shown that the joint pdf of X and Y is
f(x, y) = 2e (*+9), 0 <x<y<∞
a. Determine the marginal density of X.
b. Determine the conditional density of Y given
X = x.
c. Determine the probability that Y is greater
than 2, given that X = 1.
d. Are X and Y independent? Explain.
e. Determine the conditional mean of Y given
X = x. Is E(YIX = x) a linear function of x?
f. Determine the conditional variance of Y given
X = x.

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