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** **(**t**a,**X;**)** *= µ

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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

showing.

* *

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