a) Suppose that P and Q are two independent continuous random variables with thefollowing probability functionsf(p) = 4p for 0sps1f(a) = 5q for 0sas1i Find the probubility P(P + Qs 0.5)ii. Find the correlation coefficient (p)i. Find the conditional probability P(P < 0.2/Q < 0.25)b) The two dimensional random variables (X.Y) has a joint density function1+x+y+ cxyf(x. y) = -c+3x2 0, y 20where e > 0 is a coi. Find the probability P(X s 1)ii There exists exactly only one value of c in order that X and Y are independent.constant.What is such a value?

a) Suppose that P and Q are two independent continuous random variables with the following probability functions f(p) = 4p for Osps1 for 0sqs1 f(e) = 5q i Find the probubility P(P + Qs 0.5) ii Find the correlation coefficient (p) ii Find the conditional probability P(P < 0.2/Q < 0.25) rional mnd antion

a) Suppose that P and Q are two independent continuous random variables with the following probability functions f(p) = 4p for Osps1 for 0sqs1 f(e) = 5q i Find the probubility P(P + Qs 0.5) ii Find the correlation coefficient (p) ii Find the conditional probability P(P < 0.2/Q < 0.25) rional mnd antion

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

100%

a) Suppose that P and Q are two independent continuous random variables with the
following probability functions
f(p) = 4p for 0sps1
f(a) = 5q for 0sas1
i Find the probubility P(P + Qs 0.5)
ii. Find the correlation coefficient (p)
i. Find the conditional probability P(P < 0.2/Q < 0.25)
b) The two dimensional random variables (X.Y) has a joint density function
1+x+y+ cxy
f(x. y) = -
c+3
x2 0, y 20
where e > 0 is a co
i. Find the probability P(X s 1)
ii There exists exactly only one value of c in order that X and Y are independent.
constant.
What is such a value?

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