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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.
A researcher determines that 42.7% of all downtown office buildings have ventilation problems. Is this a statistic or a parameter; explain your answer.
A rental agent claims that the mean monthly rent,u, for apartments on the east side of town is less than$725 . A random sample of 13 monthly rents for apartments on the east side has a mean of$714
At the .01 significance level can we (she) conclude that the true average daily amount of tips is greater than $80? yes or no.....
question eighteen per cent of multinational companies provide an allowance for personal long-distance calls for
Complete the ANOVA table. Carry out a test of hypothesis on each of regression coefficients. Could you delete any of the variables?
You have money in an account at 7% interest, compounded monthly. To the nearest year, how long will it take for your money to triple?
Do the confidence interval limits contain 98.6F? What does the sample suggest about the use of 98.6F as the mean body temp.
The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. A random sample of 60 people used the new toothpaste for 6 months. The mean number of cavities at their next checkup is 1.5. In general ..
Create a 95%confidence interval for the value of the population mean, given that their is a sample mean of 49 and a standard deviation of 3 but now found those valuesfrom a sample of only 20 observations.test the hypothesis allowing for type 1 error ..
At a significance level of 0.01, can you conclude that the mean times are different? Assume each population of relief times is normally distributed and that the population variances are equal.
How much error, on average, would you expect between the sample mean (M) and the population mean for: a sample of n=4 scores, a sample of n=16 scores, and a sample of n=25 scores.
At one excavation site 8641 pot shards have been found that not yet been cleaned and identified. What is the probability that:
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