Conditional distribution: Calculate, E(XY/Y-2X=m), where m is a real number

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viti

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I have to solve this exercise:

"Let Y and X be two independent random variables identically distributed as standard normals. Calculate,

E(XY/Y-2X=m), where m is a real number"

Could anyone help me? :)
 
viti said:
"Let Y and X be two independent random variables identically distributed as standard normals. Calculate,

E(XY/Y-2X=m), where m is a real number"
Click to expand...
Does "XY/Y-2X" mean either of the following?

. . . . .\(\displaystyle \mbox{a. }\, \dfrac{XY}{Y}\, -\, 2X\)

. . . . .\(\displaystyle \mbox{b. }\, \dfrac{XY}{Y\, -\, 2X}\)

When you reply, please include a clear listing of your thoughts and efforts so far, so we can "see" where you're getting stuck. Thank you! ;)
 
stapel said:
Does "XY/Y-2X" mean either of the following?

. . . . .\(\displaystyle \mbox{a. }\, \dfrac{XY}{Y}\, -\, 2X\)

. . . . .\(\displaystyle \mbox{b. }\, \dfrac{XY}{Y\, -\, 2X}\)

When you reply, please include a clear listing of your thoughts and efforts so far, so we can "see" where you're getting stuck. Thank you! ;)
Click to expand...

The last one. I need to find the conditional expectation of XY given Y-2X=m, where m is a constant. I dont know if I need to use the following formula: f(z/k)=f(z,k)/f(k) where in this case z=XY and k=Y-2X

Thank you!
 
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