2. Let f (x, y) be the probability density function of the continuous random variable (X,Y). If U = XY, show that the probability density function of U is given by ∞0 fu (u) = 1 (².v) | | dv. 12 =00

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A: From the given information, PDF's of x1 and x2 are as given below: fx1=12,x1∈0,2fx2=x22,x2∈0,2…

Q: 5) Given X with the probability density function: 4x, if 0<x< 1 0, otherwise fx(x) 6) = Determine…

A: Check the solution in the explanation.Explanation:Check the image below for a detailed solution.

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Q: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0&lt;x&lt;3,0&lt;y&lt;3

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Q: If X is a uniformly distributed random variable in 2 find the density of 2 Y = tan X.

A: Answer: For the given data,

Q: Let X be a continuous random variable with probability density function 1 f (x) = 7(1+x² ) Define Y…

A: The mean of Y is given by: μ= E(Y) = E1X It is known that,  E1X = ∫-∞∞1xf(x) dx

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Q: 9. Is the function defined by f(x)=0 = 1 18 =0 (2x+3) x4 a probability density function? Find the…

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Q: No 9 f, ) - 8X, X2 onlyer Po.4< X - 0.2) = 2

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A: Solution-: Let, X→U(a=1,b=3) We find the probability density function of V=12eX