and let Consider a random variable X with the following distribution r 13 4 7 8 P(X=x) 0.2 0.25 0.1 0.35 0.1 1, X <3 X27 3, otherwise. Y=2, (a) What are the mean and variance of X? (b) What are the mean and variance of Y? (c) Are X and Y independent? Justify with a formula. (d) Find Cov(X, Y) and the correlation coefficient pxy.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 9E
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and let
Consider a random variable X with the following distribution
1
P(X= x) 0.2
3
0.25 0.1 0.35
1,
Y=2,
X <3
X27
3, otherwise.
(a) What are the mean and variance of X?
(b) What are the mean and variance of Y?
(c) Are X and Y independent? Justify with a formula.
(d) Find Cov(X, Y) and the correlation coefficient pxy.
8
0.1
Transcribed Image Text:and let Consider a random variable X with the following distribution 1 P(X= x) 0.2 3 0.25 0.1 0.35 1, Y=2, X <3 X27 3, otherwise. (a) What are the mean and variance of X? (b) What are the mean and variance of Y? (c) Are X and Y independent? Justify with a formula. (d) Find Cov(X, Y) and the correlation coefficient pxy. 8 0.1
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