# (a) Suppose that X1 ~ N(Î¼1, Ï12) and X2 ~ N(Î¼2, Ï22) are independently distributed. What is the variance of...

## Question:

Y = pX1 + (1 - p)X2?

Show that the variance is minimized when

What is the variance of Y in this case?

(b) More generally suppose that Xi ~ N(Î¼i, Ïƒi2), 1 ‰¤ i ‰¤ n, are independently distributed, and that

Y = p1X1 + ... + pnXn

where p1 + ... + pn = 1. What values of the pi minimize the variance of Y, and what is the minimum variance?

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## Probability And Statistics For Engineers And Scientists

**ISBN:** 9780495107576

3rd Edition

**Authors:** Anthony Hayter

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