probability distributions: bivariate normal, expon. distros

soureddy.c

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hi im struck with thz pblm........its basically my hw due within 2days.....can u please give me the solution for thz problem....?thanks a bunch

1) If X and Y have a bivariate normal distribution and U = X + Y and V = X - Y, find an expression for the correlation coefficient of U and V.

2) If X has an exponential distribution, show that P(X >= t + T \ X >= T) = P(X >= t)

This property of an exponential random variable parallels that of a geometric random variable given as [ P(X = x + n \ X > n) = P(X = x).
 
soureddy.c said:
can u please give me the solution for thz problem....?
There are a couple of folks who come through occasionally and complete students' assignments for them, but I'm afraid legitimate tutors don't generally do that sort of thing. Sorry! :oops:

It would be helpful if you showed what you have tried so far. Then the tutors will be able to "see" where you are and what sort of assistance you need. :idea:

Please be complete. Thank you! :D

Eliz.
 
1) Just do the algebra associated with the calculation of the relevant moments.
2) Use the basic definition of the conditional probability of A|B.
 
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