The joint probability mass function of the random variables X, Y, Z is p(1,2,3) = p (2,1,1) = p(2,2,1)= p(2,3,2)= Find (a) E[XYZ] (b) E[XY+XZ+YZ]

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A: * SOLUTION :-  Based on the above information we prove that X and Y are independent random…

Q: (a) What is the probability density function of aX + bY? (b) Compute E[X|X − 2Y] and E[X²|X – 2Y].

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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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A: From the given information, the joint probability mass function for X and Y is,

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A: The cumulative mass function for X is given by: FXx=PX≤x for -∞≤x≤∞

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A: Solution: From the given information, the probability mass function of X and Y is

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A:

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A: Step 1: Step 2: Step 3: Step 4:

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Q: D,E, F

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A: Solution

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Q: What is P(X=0,Y=2)?

A: From the given information, P(X=0, Y=0)=P(X=1. Y=2)=0.

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A: