3. Suppose the conditional distribution of Y given X = x is expoential with rate x, i.e., frpx-(y)xe-y 0 yo0, and suppose the marginal distribution of X is a gamma distribution with parameters n and A, where n > 2 is an integer and A > 0 is the rate, with the following pdf -n-1e- fx(x) r(n)

3. Suppose the conditional distribution of Y given X = x is expoential with rate x, i.e., frpx-(y)xe-y 0 yo0, and suppose the marginal distribution of X is a gamma distribution with parameters n and A, where n > 2 is an integer and A > 0 is the rate, with the following pdf -n-1e- fx(x) r(n)

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

a) compare E(Y|X=x) and E(Y|X)

b) Find the pdf of Y

c) find the conditional pdf of X given that Y=y

3. Suppose the conditional distribution of Y given X = x is expoential with rate x, i.e.,
frpx-(y)xe-y
0 yo0,
and suppose the marginal distribution of X is a gamma distribution with parameters n
and A, where n > 2 is an integer and A > 0 is the rate, with the following pdf
-n-1e-
fx(x)
r(n)

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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