Posted by **amelie** on Sunday, April 20, 2008 at 7:56pm.

In a study of particulate pollution in air samples over a smokestack, X1 represents the amount of pollant per sample when a cleaning device is not operating, and X2 represents the amount per sample when the cleaning device is operating. Assume that (X1, X2) has a joint probability density function.

f(X1,X2) =[ 1 for 0<=X1<=2 0<=X2<=1

2 X2<=X1

[ 0 ELSEWHERE

The random variable Y=X1-X2 represents the amount by which the weight of emitted pollutant can be reduced by using the cleaning device.

a) Find E(Y) AND V(Y)

I have solved the E(Y)already.But I

have problems with the variance.

Work

=========

a) E(Y)= 1

E(X1)=2 E(X2)=1

V(Y)= V(X1-X2)= V(X1)-V(X2)

V(X1)= E(X1 ^2) - E(X1) ^2

= ç(FROM 0 TO 2) X1^2 dX1 - 4

= -1 1/3

V(X2)= ...

= ç(FROM 0 TO 1) 2X2 ^2 dX2 - 1

= -1/3

ANS= -1, WRONG

CORRECT ANS= 1/6

i though i was doing the work correctly until i got negative variances, can you help me figure out what am i going wrong.

- yarmouk -
**sami**, Wednesday, April 17, 2013 at 4:00pm
E[y]=3/2

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