Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

Consider a continuous random vector (Y, X) with joint probability density function

f(x, y) = 1 for 0 < x < 1, x < y < x + 1.

What is the marginal density of X and Y? Use this to compute Var(X) and Var(Y)
Compute the expectation E[XY]
Use the previous results to compute the correlation Corr (Y, X)
Compute the third moment of Y, i.e., E[Y³]

Expert Solution

orchestra answered 1 year ago

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1 for 0 < x < 1, x < y < x + 1. A. What is the marginal density of X and Y ? Use this to compute Var(X) and Var(Y). B. Compute the expectation E[XY] C. Use the previous results to compute the correlation Corr(Y, X). D. Compute the third moment of Y , i.e., E[Y3].

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Let (X, Y) be a random vector with a function of the joint density given by...

Let (X, Y) be a random vector with a function of the joint density given by ˜ fX, Y (x, y) = k (2x + y) I (2,6) (x) I (0.5) (y) a) Determine k so that f X, Y (x, y) is a true probability density function joint quality. b) Determine the marginal probability density functions of X and Y. c) Calculate P (3 <X <4, Y> 2). d) Calculate P (X + Y> 4).

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Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

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