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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.

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.

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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(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 up to 3rd decimal place. (You shall use calculator to complete this problem.) Suppose two random variables X, Y admits density f(x, y) = 9 -x-3y 7(2x+y)e¯ " x, y ≥ 0, and f(x, y) = 0 for other (x, y). Compute the covariance of X, Y. Use the result to decide which of the following holds: Var[X + Y] < Var[X] + Var[Y], or =, or >.
Transcribed Image Text:(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 up to 3rd decimal place. (You shall use calculator to complete this problem.) Suppose two random variables X, Y admits density f(x, y) = 9 -x-3y 7(2x+y)e¯ " x, y ≥ 0, and f(x, y) = 0 for other (x, y). Compute the covariance of X, Y. Use the result to decide which of the following holds: Var[X + Y] < Var[X] + Var[Y], or =, or >.
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