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A dormitory has n students, all of whom like to gossip. One of the students hears a rumor, and tells it to one of the other n -1 students picked at random. Subsequently, each student who hears the rumor tells it to a student picked at random from the dormitory (excluding, of course, himself/ herself and the person from whom he/ she heard the rumor). Let pr be the probability that the rumor is told r times without coming back to a student who has already heard it from a dormitory mate. So p1 = p2 = 1, and pn = 0.
a) Find a formula for pr for r between 3 and n - 1.
b) Estimate this probability for n = 300 and r = 30.
Suppose 70 managers selected randomly in the United States are interviewed. What is the probability that fewer than 35 use self-directed work teams.
a) Given a random variable x with mean 10 and variance 9, find the expected value and variance of the random variable y where y = 12 + 2x.
Determine the standard error of the sampling distribution of the mean for simple random samples with the sample sizes:- n=16.
a random sample of size n is to be used to test the null hypothesis that the parameter theta of an exponential
Explain the importance of random sampling. What problems/limitations could prevent a truly random sampling and how can they be prevented?
Suppose that the company is willing to consider dropping the distribution center limitations; that is, customers could be served by any of the distribution centers for which costs are available. Can costs be reduced? By how much - If the company d..
Calculate the mean and standard deviation of the simulated values. How do they compare to the mean and standard deviation of the given probability distribution?
Let the independent r.v.'s X1,. .., Xn be distributed as U(0, 1), and let 1 j n. Use the relevant results in Example 3, and Exercise 1.6(i) in order to derive: i) The conditional p.d.f. of Yj, given Y1;
Construct a 95% confidence interval estimate for the population proportion of airline travelers who think that the airline fee that is most unreasonable is additional charges to redeem point/miles.
an experiment was conducted to determine the performance of two varieties of wheat at seven randomly chosen
Will increasing sample size (n) increase or decrease the value of standard error? Will this increase or decrease power?
Provide an explanation of a chi-square test. Why would you use the chi-square statistic? What type of data is used with chi square analysis?
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