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OFDM
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I'm having a problem evaluating a distribution-
Suppose X and Y are Chi-square random variables, and a is some
constant greater than 0. X and Y are independent, but not identically distributed (they have different DOFs).
I want to find
P(X>a,X-Y>0). So I use Bayes' theorem to write
P(X>a,X-Y>0)
=P(X>a | X-Y > 0)*P(X-Y>0)
=P(X>a| X>Y)*P(X>Y)
Now I have an expression for P(X>a) and P(X>Y), but I am at a
loss as to how to evaluate the conditional distribution P(X>a|
X>Y).
I figured out that if Y was a constant (rather than a random variable), then I could write
P(X>a| X>Y) = { 1 if Y>a
{ P(X>a)/P(X>Y) if Y<a
But this does not help evalaute the distribution because I requires knowledge of the value of random variable Y.
Any help will be much appreciated.
Suppose X and Y are Chi-square random variables, and a is some
constant greater than 0. X and Y are independent, but not identically distributed (they have different DOFs).
I want to find
P(X>a,X-Y>0). So I use Bayes' theorem to write
P(X>a,X-Y>0)
=P(X>a | X-Y > 0)*P(X-Y>0)
=P(X>a| X>Y)*P(X>Y)
Now I have an expression for P(X>a) and P(X>Y), but I am at a
loss as to how to evaluate the conditional distribution P(X>a|
X>Y).
I figured out that if Y was a constant (rather than a random variable), then I could write
P(X>a| X>Y) = { 1 if Y>a
{ P(X>a)/P(X>Y) if Y<a
But this does not help evalaute the distribution because I requires knowledge of the value of random variable Y.
Any help will be much appreciated.
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