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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.
randomly selected nonfatal occupational injuries and illnesses are categorized according to the day of the week that
How many more days should be included in the sample to be 95% sure the population mean μ is within $50 of the sample mean x?
you are invited to play the following game. you may repeatedly roll a fair six-sided die unless you roll a one at which
twenty years ago postal employees worked for the postal service an average of 7.5 years. recently a sample of 100
The GMAT scores of MBA students is assumed to be distributed normally with a mean of 530 and a standard deviation of 80. The GMAT scores of ten students are selected randomly.
The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation
What control chart(s) would you use for this data and what are the final control limits?
a new phone answering system is capable of handling 6 calls every 10 minutes. prior to installing the new system
if a person bought 1 share of google stock within the last year what is the probability that the stock on that day
What is the response variable? Is this an experimental study or an observational study? Explain your answer in at most 25-30 words.
We recalculated our comparison of ideal number of children, this time only for women, separating them into two groups, those who indicated that they were "very happy" or "not at all happy" with life.
Using the six-step critical value approach, at the 0.05 level of significance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 25 minutes?
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