Consider two binary random variables X and Y, i.e. they take values in R = {0, 1} You are told that P(X = 0) = 1/3 and P(Y = 1) = 1/3, and that the probabilit that X and Y have the same value is P(X =Y) = 1/2. %3D

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A: It is an important part of statistics. It is widely used.

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A: the joint PMF of random variables X and Y is:- P(X=x,Y=y) = a(x+y);   { (x,y) : {4,5,6} x {1,2,3}  }…

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Q: There are three random variables X, Y and Z,for which we know the following information E(X)= 6,…

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A: Given E(XY)=0, E(X)=0, E(Y)=3  Farmula used Cov(X,Y)=E(XY)-E(X)E(Y)

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A: a)It is given that, .

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A: We can get the mean and variance after finding the first and second derivative of mgf at t= 0

Q: = 1- Q(x).

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A: Given,E(X)10Var(X)=4E(Y)=12Var(Y)=3W=-2X+Y X and Y are independent.

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Q: Suppose the joint PMF of the random variables X and Y is P(X= x, Y = y) = a(x+y) if(x, y) = {1,2,3}…

A: the joint PMF of X and Y:- P(X=x, Y=y) = a(x+y);   (x,y): {1,2,3}x{2,3,4}