The Distribution of a Linear Combination
Message posted by William H. on November 22, 2000 at 12:00 AM (ET)

Can people explain the subject and also teach me how to solve the example below..thank you!!

X1~N(5,10)
X2~N(3,8)
Cov(X1,X2) = 2
Y=X1-X2

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Re: The Distribution of a Linear Combination
Message posted by Phil on November 22, 2000 at 12:00 AM (ET)

Linear combinations of r.v.s is not that easy to teach. In the case of normal r.v.s, their sums and difference happen to be normal also.

The mean of Y = 5-3
The variance of Y = var x1 + var x2 - 2(cov x1,x2)
(and assuming the second parameter you gave was the variance):
Therefore var Y = 8 + 10 - (2)(2) = 14

You may need to reference a mathematical statistics book.