(2) The joint p.d.f of the random variables X and Y is e-x-y, x>0, y > 0, { f(x, y)= 0, otherwise. (a) Find the marginal p.d.f.s of X and Y. (b) Find the mean of X, μx and the mean of Y, µy. (c) Find the variance of X, o and the variance of Y, oz. (d) Given Y = y, find the conditional p.d.f. of X, f(x|y). (e) Find E[X|y], for 0 < y. (f) Find o, for 0
(2) The joint p.d.f of the random variables X and Y is e-x-y, x>0, y > 0, { f(x, y)= 0, otherwise. (a) Find the marginal p.d.f.s of X and Y. (b) Find the mean of X, μx and the mean of Y, µy. (c) Find the variance of X, o and the variance of Y, oz. (d) Given Y = y, find the conditional p.d.f. of X, f(x|y). (e) Find E[X|y], for 0 < y. (f) Find o, for 0
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
Related questions
Question
please make sure to answer questions b,e,f
![(2)
The joint p.d.f of the random variables X and Y is
exy, x>0, y > 0,
f(x, y) =
0,
(a) Find the marginal p.d.f.s of X and Y.
(b) Find the mean of X, ux and the mean of Y, µy.
(c) Find the variance of X, o and the variance of y, o.
(d) Given Y = y, find the conditional p.d.f. of X, f(xy).
(e) Find E[X|y], for 0 <y.
(f) Find o for 0 < y.
(g) Find the covariance C[X,Y]
otherwise.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2F303b28e5-c90a-4f1a-b095-712878f553cb%2Fr3cfi6_processed.png&w=3840&q=75)
Transcribed Image Text:(2)
The joint p.d.f of the random variables X and Y is
exy, x>0, y > 0,
f(x, y) =
0,
(a) Find the marginal p.d.f.s of X and Y.
(b) Find the mean of X, ux and the mean of Y, µy.
(c) Find the variance of X, o and the variance of y, o.
(d) Given Y = y, find the conditional p.d.f. of X, f(xy).
(e) Find E[X|y], for 0 <y.
(f) Find o for 0 < y.
(g) Find the covariance C[X,Y]
otherwise.
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