On Tue, 1 Jul 2003 11:55:25 +0800, "ZHANG Yan" <[EMAIL PROTECTED]>
wrote:
> Maybe I have not stated the question clearly.
>
> A positive random variable X varies in the range [a,b] with pdf f_X(x).
> Suppose a real number r greater than a and less than b, i.e. a<r<b. A value
> of the random variable will fall in the range [a,r] or the range [r,b].
> Define the event
>
> A = value of random variable falls in the range [a,r];
> B = value of random variable falls in the range [r,b];
>
> Then, how to compute the expected value of X with the value in the range
> [a,r] and in the range [r,b]. namely, to find
>
> E(X|A) and E(X|B)
You stated your question clearly and I'm going to repeat my answer
A
Integral x*f_X(x) dx
a
E(X|A) = --------------------
A
Integral f_X(x) dx
a
b
Integral x*f_X(x) dx
A
E(X|B) = ------------------
b
Integral f_X(x) dx
A
assuming that f_X ist continuous and Pr(A) and Pr(B) are not 0.
Regards
Horst
.
.
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