On Wed, 16 Jul 2003 16:38:40 +0800, "ZHANG Yan" <[EMAIL PROTECTED]>
wrote:
> Hea, I am asking for a question about the expected value.
>
> Suppose the postive continuous random variable X, Y, Z1, Z2,Z3,Z4. Moreover,
> Y, Z1,Z2,Z3,Z4 are independent. The pdf of them are given. They satisfy the
> following relationship.
>
> __
> | Y if Y<Z
> X =
> | Z1 if 2Z>Y>Z
> | Z2 if 3Z>Y>2Z
> | Z3 if 4Z>Y>3Z
> | Z4 other
> ---
>
> I need to find the expected value of X. What should I do?Thanks in advance!
I assume that Z is some constant. and y(t) is the pdf of Y.
Using
Z
p0 = Pr {Y<Z} = int y(t) dt
-oo
2Z
p1 = Pr {Z<Y<2Z} = int y(t) dt
Z
3Z
p2 = Pr {2Z<Y<3Z} = int y(t) dt
2Z
4Z
p3 = Pr {3Z<Y<4Z} = int y(t) dt
3Z
oo
p4 = Pr {4Z<Y} = int y(t) dt
4Z
(Sum p_i = 1)
Then E(X) = p0*E(Y)+p1*E(Z1)+p2*E(Z2)+p3*E(Z3)+p4*E(Z4)
It is immaterial whether Y,Z1,Z2,Z3,Z4 are independent or not. If for
instance Y=Z1=Z2=Z3=Z4 then E(X)=E(Y).
Regards
Horst
.
.
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