Let X,Y be continuous random variables with joint density function if 0 < x < 1,x < y < 1 f (x, y) = { 8xy otherwise. Calculate the covariance of X and Y.

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

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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A: Independence of pdf applied.

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A:

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A: From the given information, f(x, y)=k(x+4y), 0&lt;x&lt;2, 0&lt;y&lt;1 The value of k is obtained…

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A:

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

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Q: Suppose that Var(X) = 3, Var(Y ) = 4, and Cov(X,Y ) = 1. (a) Find Cov(2X −Y,X + 3Y ). (b) Find…

A: Solution-: Given: Var(X)=3, Var(Y)=4, Cov(X,Y)=1 We want to find, (a) Cov(2X-Y, X+3Y)=? (b)…

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A: The probability density function is given as,

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A: Let's break down the computation of the covariance Cov(Ys, Yt) for the OU process into steps:Step 1:…

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A: Since you have posted a question with multiple sub-parts, we will solve the first two sub-parts for…

Q: e joint density of X and Y is given by, fxr (x, y) = (x² + 0 1) b) Find the marginal probability…

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

Q: Determine the value of c that makes the function f(x, y) = c(x + y) a joint probability mass…

A: f(x,y)=c(x+y)   ; x=1,2,3 and y=1,2,3