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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.
Mention the experimental outcomes. Illustrate out a random variable threat that represents the number of heads occurring on the two tosses.
If Taco Bell costs $3 and a home lunch costs $1 and the Springdale room is free, then how much lunch budget should he allow for his semester, which includes 100 lunches?
A chemical engineer desiring to study the evaporation rate of water from brine evaporation beds obtained data on the number of inches of evaporation in each of 55 July days spread over 4 years. Find the sample mean
Which of the examples below represent the Ratio level of scaling?
A report states that 73% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 0.03 with 98% confidence?
Using the z-score of ±1.645 for the 5 percent cutoff and the z-score of ±1.96 for the 2.5 percent in the tail, identify the subject identification (ID) number for subjects who are closest to the cutoff for the upper 2.5 percent and 5 percent of th..
a news article reports that americans have differing views on two potentially inconvenient and invasive practices that
Ffind the mean, variance and standard deviation of binomial distribution? what valuses of the random variable X would you consider unusual?
according to the school board 48 of all the voters in the district support the refeendum. suppose a principal is
Test whether the signals are uniformly distributed over the 24-hour period.
Students in the social work course received the following course grades. Create a frequency distribution for this data. Compute the mean. Determine the median.
The joint cumulative distribution function for (X, Y) is given by F(x, y) = ( 1 - e-x/ID - e-y/l + e-lx+SyJ/I0)/10,001 (x)I10,oodY). a. Find the joint density function of (X, Y).
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