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a) Suppose that X and Y are two independent continuous random variables with the following probability functions f(x) = 2x f(y) = 3y? for 0sx<1 for 0 sys1 i. Find the probability P(X + Y S 0.5) ii. Find the covariance (X, Y). iii. Find the conditional probability P(X < 0.2/Y < 0.25) b) The two dimensional random variables (P,Q) has a joint density function 1+p+q+ cpq f(p, q) =: .e-(p+a), p2 0, q 2 0 c+3

a) Suppose that X and Y are two independent continuous random variables with the following probability functions f(x) = 2x f(y) = 3y? for 0sx<1 for 0 sys1 i. Find the probability P(X + Y S 0.5) ii. Find the covariance (X, Y). iii. Find the conditional probability P(X < 0.2/Y < 0.25) b) The two dimensional random variables (P,Q) has a joint density function 1+p+q+ cpq f(p, q) =: .e-(p+a), p2 0, q 2 0 c+3

A First Course in Probability (10th Edition)
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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a) Suppose that X and Y are two independent continuous random variables with the following probability functions f(x) = 2x for 0Sxs1 f() = 3y² for 0 <ys1 i. Find the probability P(X + Y < 0.5) ii. Find the covariance (X, Y). ii. Find the conditional probability P(X < 0.2/Y < 0.25) b) The two dimensional random variables (P,Q) has a joint density function 1+p +q+ cpq f(p, q) = .e-(p+q), p 2 0, q > 0 c +3
Transcribed Image Text:a) Suppose that X and Y are two independent continuous random variables with the following probability functions f(x) = 2x for 0Sxs1 f() = 3y² for 0 <ys1 i. Find the probability P(X + Y < 0.5) ii. Find the covariance (X, Y). ii. Find the conditional probability P(X < 0.2/Y < 0.25) b) The two dimensional random variables (P,Q) has a joint density function 1+p +q+ cpq f(p, q) = .e-(p+q), p 2 0, q > 0 c +3
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