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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 27T
Related questions
Question
![(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 >.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4f6fb5f-9dce-46e9-a62a-df8f162ca2bd%2Fe42b4377-332c-41c2-868d-277f3c8fa46f%2Faaprne_processed.jpeg&w=3840&q=75)
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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