##### Question

In: Statistics and Probability

# 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).

## Solutions

##### Expert Solution    please note that I(0.5) is improper representation for defining range, so assuming the correction to be as I(0,5) the question has been solved.

Thanks!

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