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Chapter 6: Q.6.3 (page 275)
Suggest a procedure for using Buffon’s needle problem to estimate π. Surprisingly enough, this was once a common method of evaluating π.
Knowing L and D we can calculate.
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Verify Equation .
A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at a time, until the defective ones are identified. Denote by N1 the number of tests made until the first defective is identified and by N2 the number of additional tests until the second defective is identified. Find the joint probability mass function of N1 and N2.
According to the U.S. National Center for Health Statistics, 25.2 percent of males and 23.6 percent of females never eat breakfast. Suppose that random samples of 200 men and 200 women are chosen. Approximate the probability that
(a) at least 110 of these 400 people never eat breakfast;
(b) the number of the women who never eat breakfast is at least as large as the number of the men who never eat breakfast.
Three points are selected at random on a line . What is the probability that lies between ?
Let W be a gamma random variable with parameters (t, β), and suppose that conditional on W = w, X1, X2, ... , Xn are independent exponential random variables with rate w. Show that the conditional distribution of W given that X1 = x1, X2 = x2, ... , Xn = xn is gamma with parameters t + n, β + n i=1 xi .
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