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).

Expert Solution

orchestra answered 1 year ago

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

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