Let X and Y have the joint probability density function f(x, y) = 5, for 0 < x < y < 1. (i) Find the marginal probability density function of X and Y. (ii) Find the conditional probability density function of X, given Y = y. (iii) Find the conditional mean of X, given Y = y.

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Q: (d) Are the random variables X and Y independent? Justify your answer.

A: To check independence of X and Y we have to find marginal pdfs of X and Y.

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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: The formula to calculate the expected value of x is,The formula to calculate variance of x is,

Q: Let X and Y have a bivariate normal distribution with mean vector (₁ = 3, μ2 = 1)', and standard…

A: The answer to the first sub question is 4.Please follow the below attachment for the solution.

Q: Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy…

A: Answer: The covariance between X and Y can be calculated as follows:  Cov(X, Y) = E[(X - E(X))(Y -…

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A: X and Y are two independent random variables,  f(x)=e-x , x&gt;00     , o.wf(y)=e-y  , y&gt;00…

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A: Solution:-

Q: Sk(x + 4y) ,0 <x < 2, 0 < y < 1 ,otherwise Let f(x,y) = be the joint probability density of X and Y.

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: Given: fx, y=ce-6xe-3y               0&lt;y&lt;x

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Q: Suppose that the random variables X and Y have the following joint probability density function.…

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