Thread: joint distribution

Originally Posted by szpengchao

Here is some direction:

The thread below contains the ideas you need for the first part:

http://www.mathhelpforum.com/math-he...-function.html


For the second part, you should know how to get the pdf of Y/2 from the pdf of Y ...... And you should know that the pdf of the sum of two random variables is the convolution of their seperate pdf's.

To get the pdf of the random variable max(X, Y), use the same idea that I used in my reply to your question about showing
E(U) = 1/3.

so, i got the density of X+1/2 Y = lambda /2 * e^(-lambda y)

and i got density for max : lambda square * e^(-lamda( x+y))

is it true??
please check

Originally Posted by szpengchao

What's wrong is that the upper integral terminal is wrong (the lower one is correct, but probably by accident).

The U and V take on values in the region defined by X > 0 and Y > 0, that is, the region defined by U > 0 and 2V - U > 0. Sketch this region. Then you'll see that the integral terminals are U = 0 (lower) and U = 2V (upper).

You should check your final answer by:

1. Finding the pdf g(x) for Y/2, and

2. Calculating the convolution f(x) * g(x) (you'll need to be careful with the integral terminals).

Originally Posted by szpengchao

so, i got the density of X+1/2 Y = lambda /2 * e^(-lambda y)

and i got density for max : lambda square * e^(-lamda( x+y))

is it true??
please check

It's much easier (for me at least) to check your answers by looking over your working .....