Question

In: Statistics and Probability

If X and Y are independent exponential random variables, each having parameter λ = 6, find...

If X and Y are independent exponential random variables, each having parameter λ = 6, find the joint density function of U = X + Y and V = e^2X.

The required joint density function is of the form

f_U,V(u, v) =

{	g(u, v)	u > h(v), v > a
{	0	otherwise

(a)	Enter the function g(u, v) into the answer box below.

(b)	Enter the function h(v) into the answer box below.

(c)	Enter the value of a into the answer box below.

Expert Solution

Solution:-

Given that

x and y are exponential random variable each having parameter .

density function of X,

joint density of x, y

, x> 0, y > 0

,

(x and y are independent)

By the method of transforms on

f(u, v) is the joint density of u and v

(a)

Enter the function g(u, v) into the answer box below

(a)

so

(b)

Enter the function h(v) into the answer box below.

So the function h(v) is given that

(c)

Enter the value of a into the answer box below.

value of "a" into the answer box below

a = 1

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orchestra answered 1 year ago

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