3.9.S. Suppose that X; is a random variable for which E(X;) = 11, i = 1, 2, . .., n. Under what
conditions will the following be true?
E (ta,X;) = µ
3.9.6. Suppose that the daily closing price of stock goes up an eigh th of a point with probability p and down an eighth of a point with probability q, where p > q.After n days how much gain can we expect the stock to have achieved? Assume that the daily price fluctuations are independent events.
3.9.7. An um contains r red balls and w white balls. A sample of n balls is drawn in order and
without replacement. Let X; be 1 if the ith draw is red and O otherwise i = 1, 2, ... , 11.
(a) Show tha t E(Xi) = £(X 1), i= 2, 3, ...,n
(b) Use the Corollary to Theorem 3.9.2 to show that the expected number of red balls
is nr/ (r + w).
3.9.8. Suppose two fair dice are tossed. Find the expected vaJue of the product of the faces
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