a) Suppose that X and Y are two independent continuous random variables with thefollowing probability functionsf(x) = 2x for 0sxs1fV) = 3y² for 0sys1i. Find the probability P(X +Y < 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 function1+p+q+cpq e-(p+4),f(p, q) =p 2 0,9 20c+3where c> 0 is a coi. Find the probability P(P < 1)ii. There exists exactly only one value of c in order that P and Q are independent.What is such a value?constant.

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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 0sx<1 fO) = 3y? for 0sys1 i. Find the probability P(X +Y < 0.5) ii. Find the covariance (X, Y). iii. Find the conditional probability P(x s 0.2/Y s 0.25) b) The two dimensional random variables (P.Q) has a joint density function f(p. g) =1+P+q+ cpq-p+g) c+3 p 2 0,q 20 where c > 0 is a ce constant. i. Find the probability P(P < 1) ii. There exists exactly only one value of c in order that P and Q are independent. What is such a value?

a) Suppose that X and Y are two independent continuous random variables with the following probability functions f(x) = 2x for 0sx<1 fO) = 3y? for 0sys1 i. Find the probability P(X +Y < 0.5) ii. Find the covariance (X, Y). iii. Find the conditional probability P(x s 0.2/Y s 0.25) b) The two dimensional random variables (P.Q) has a joint density function f(p. g) =1+P+q+ cpq-p+g) c+3 p 2 0,q 20 where c > 0 is a ce constant. i. Find the probability P(P < 1) ii. There exists exactly only one value of c in order that P and Q are independent. What is such a value?

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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