If the joint probability density function of the random variables X and Y is given by...

If the joint probability density function of the random variables X and Y is given by f(x, y) = (1/4)(x + 2y) for 0 < x < 2, 0 < y < 1, 0 elsewhere

(a) Find the conditional density of Y given X = x, and use it to evaluate P (X + Y/2 ≥ 1 | X = 1/2)

(b) Find the conditional mean and the conditional variance of Y given X = 1/2

(c) Find the variance of W = X − 2Y + 3

(d) Find the covariance of X and Y, and determine if X and Y are independent

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orchestra answered 1 year ago

The joint probability density function for two random variables X and Y is given as, fx,y...

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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).

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

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The joint density function for random variables X, Y, and Z is f(x, y, z)= Cxyz if...

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If the joint probability density function of the random variables X and Y is given by...

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