(d)Let X, Y be independent Poisson random variables with X~ Poisson(1.5),Y~ Poisson (0.5). Compute the probability P(X + Y ≤ 2). Express your answer upto 3rd decimal place.(You shall use calculator to complete this problem.) Suppose two randomvariables X, Y admits densityf(x, y)=9-x-3y7(2x+y)e¯"x, y ≥ 0,and f(x, y)= 0 for other (x, y). Compute the covariance of X, Y. Use the result todecide which of the following holds: Var[X + Y] < Var[X] + Var[Y], or =, or >.

C and D are two different questions So i am solving first C

Answered: Let X, Y be independent Poisson random…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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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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Let X, Y be independent Poisson random variables with X~ Poisson (1.5), Y~ Poisson (0.5). Compute the probability P(X + Y ≤2). Express your answer up to 3rd decimal place.