# Math Help - normal distribution

1. ## normal distribution

need help with this dont know were to start

question

suppose X1 and X2 are identically distributed independent standard normal random variables
$
\mu =0, \sigma =1
$

write down the joint pdf of (X1, X2). determine the pdf of the linear transformation y1 =2x1-x2, y2=x1-2x2.

determine the correct range of this random variable.

any help appreciated

Then you solve for X1 and X2 in terms of the Y's.
You substitute into the first density and you multiply the absolute value of the jacobian.
This is just like the change to polar in calc3.

3. thanks

but how do you solve for x1 and x2.

4. Originally Posted by kermit
thanks

but how do you solve for x1 and x2.

$y_1 = 2x_1 - x_2$ .... (1)
$y_2 = x_1 - 2x_2$ .... (2)