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Unformatted text preview: STAT 333 Assignment 1 Due: Thursday October 6 at the beginning of class 1. Suppose four computers are joined in a network according to the following diagram. (The double lines indicate two separate connections.) Each connection has probability p of being broken at any time, independent of the other connections. We say a computer is “isolated” if all connections to it are broken. a. Find the probability that any one computer is isolated b. Find the probability that both computers 1 and j are isolated, for j = 2, 3, 4 c. Using the above, and an appropriate set of indicator variables, find the mean and variance of the total number of isolated computers. d. Describe how the mean and variance vary with respect to p , and provide a brief logical explanation. 2. Let ¡ ¢ £ ¡ , ¤ ¥ ¦ be the probability that a family has exactly ¤ children. Suppose that all orderings, by sex, of those n children are equally probable....
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- Fall '08
- Probability, Probability theory, one year, two days, three days, p.m.f.