(a) Suppose that X1 ~ N(Î¼1, Ï12) and X2 ~ N(Î¼2, Ï22) are independently distributed. What is the variance of...
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, Ïi2), 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?
This problem has been solved!
Step by Step Answer: