Q2) The joint probability function of two discrete random variables X and Y is given by Rx,y) = c(2x+y),where x and y can assume all integers such that 0 s xS2,0s ys3,and Ax,y) = 0 otherwise. (a) Find the value of the constant e (b) Cov (X, Y), (c) p.

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A: Given the pdf of the independent random variables X and Y as fXx=2x , 0<x<1 fYy=1 ,…

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A: X and Y are random variables such that,

Q: If X and Y are independent, then what is the probability of the event Y > 4X?

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Q: Find fQ|X (q|x) for x ∈ {0, 1} and all q.

A: It is a fact of statistics. It is widely used.

Q: -, P(T|R) P(RT) 9 Consider two events R and T. Find- 1)P(R' UT) = ? = 3 2/7,P( ,P(ROT) = 116 8

A: From the provided information,

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A:

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A: It is given that the X and Y be random variables and let a and b be constants.

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A: We have given that a joint pdf of variables X and Y.

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A:

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A: Covariance is given by, Cov(X1,X2)= E(X1)*E(X2)-E(X1*X2) E(X1)= (summation X1*p(X1,X2)) =…

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A:

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A:

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A: Step 1: Step 2: Step 3: Step 4:

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A:

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Q: 2. Let X and Y be random variables, and let a and b be constants. (a) Starting from the definition…

A:

Q: X and Y are independent, X ~U(0,1) and Y~U(0,1). Calculate the probability P(X+Y<1.5).

A: X ~U(0,1) , and Y ~U(0,1) , independently.  Then the joint distribution of X and Y, also follows,…