Let X and Y are random variables having the sample spaces X = y = {0, 1}. We have the following joint distribution function for X and Y: Fx,Y (r, y) = 0.3 if r = 0, y = 0 = 0.1 if a = 1, y = 0 = 0.4 if a = 0, y = 1 = 0.2 if a = 1, y = 1. (1) Please find the marginal distributions of X and Y, respectively ? Fx(r) =? if a = 0, Fx(x) =? if a = 1, Fy(y) =? if y = 0, Fy(y) =? if y = 1. (2) Please find the mean and variance of X. (3) Please find the conditional distribution of X given Y = 1.

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Let X and Y are random variables having the sample spaces X = y = {0, 1}. We have the following
joint distribution function for X and Y:
Fx.y (x, y) = 0.3 if x = 0, y = 0
= 0.1 if r = 1, y = 0
= 0.4 if z = 0, y = 1
= 0.2 if r = 1, y = 1.
(1) Please find the marginal distributions of X and Y, respectively ?
Fx(x) =? if r = 0,
Fx(x) =? if r = 1,
Fy(y) =? if y = 0,
Fy(y) =? if y = 1.
(2) Please find the mean and variance of X.
(3) Please find the conditional distribution of X given Y = 1.
(3) Please find the conditional distribution of X given Y = 1.
Fx|y (x|1) =? if æ = 0,
Fx|Y (x|1) =? if a = 1.
Note that Fxy(x|y) = P(X = x|Y = y).
(4) Please find the conditional expectation of X given Y = 1.
E(X|Y = 1) =?
(5) Show the relation E[X] = P(X = 1).
Transcribed Image Text:Let X and Y are random variables having the sample spaces X = y = {0, 1}. We have the following joint distribution function for X and Y: Fx.y (x, y) = 0.3 if x = 0, y = 0 = 0.1 if r = 1, y = 0 = 0.4 if z = 0, y = 1 = 0.2 if r = 1, y = 1. (1) Please find the marginal distributions of X and Y, respectively ? Fx(x) =? if r = 0, Fx(x) =? if r = 1, Fy(y) =? if y = 0, Fy(y) =? if y = 1. (2) Please find the mean and variance of X. (3) Please find the conditional distribution of X given Y = 1. (3) Please find the conditional distribution of X given Y = 1. Fx|y (x|1) =? if æ = 0, Fx|Y (x|1) =? if a = 1. Note that Fxy(x|y) = P(X = x|Y = y). (4) Please find the conditional expectation of X given Y = 1. E(X|Y = 1) =? (5) Show the relation E[X] = P(X = 1).
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