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1. Toss a fair die repeatedly. Let Sn denote the total of the outcomes through the nth toss. Show that there is a limiting value for the proportion of the first n values of Sn that are divisible by 7, and compute the value for this limit. Hint : The desired limit is an equilibrium probability vector for an appropriate seven state Markov chain.
2. Let P be the transition matrix of a regular Markov chain. Assume that there are r states and let N (r) be the smallest integer n such that P is regular if and only if PN (r) has no zero entries. Find a finite upper bound for N (r). See if you can determine N (3) exactly.
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Each contact will result in either no sale or a $50,000 sale, with the probabilities .9 and .1, respectively. Give the probability distribution for daily sales. Find the mean and standard deviation of the daily sales.
Find the critical value for a two tailed F-test with alpha=.05 when the sample size from which the variance for the numerator was obtained was 21 and the sample size from which the variance for the denominator was obtained 12
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The dice game craps is played as follows. The player throws two dice, and if the sum is seven or eleven, then he wins. If the sum is two, three, or twelve, then he loses. If the sum is anything else, then he continues throwing until he either thro..
Replacement times for CD players are normally distributed with mean of 7.1 years and a standard deviation of 1.4 years (based on data from "Getting Things Fixed," Consumer Reports). Find the probability that a randomly selected CD player will have..
to test the hypothesis h0 ? 100 vs. h1 ? gt 100 a z-score of 2.8 is calculated. the value of 2.8 isa the test
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