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 0sqs1 i Find the probubility P(P + Qs 0.5) ii Find the correlation coefficient (p) ii Find the conditional probability P(P S 0.2/Q s 0.25)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Solve the part a for me just part a

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?
Transcribed Image Text: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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