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1. * (Pepy's Problem). Find the probability that at least n sixes are obtained when 6n fair dice are rolled. Write a formula for it, and compute it for 1 ::: n ::: 5. Do you see a pattern in the values?
2. In repeated rolling of a fair die, find the minimum number of rolls necessary in order for the probability of at least one six to be
(a) > :5:
(b) > :9:
2. * In repeated rolling of a fair die, find the minimum number of rolls necessary in order for the probability of at least k sixes to be > :9 when k D 2; 3.
3. (System Reliability). A communication system consists of n com- ponents, each of which will independently function with probability p. The total system will be able to operate effectively if at least half of its components function. For what values of p is a five-component system more likely to operate effectively than a three-component system?
If we assume that the download times are normally distributed, what percent of users will wait between 5 and 10 seconds for the homepage to download?
question the following information is available.h0 mu le 10h1 mu gt 10the sample mean is 12 for the sample
Suppose we estimate this model with OLS, and there is a correlation between unobserved student traits (in the error term) with attendance. How does this bias the coefficient of attendance?
Find the probability that the number who say oatmeal is their favorite cookie is (a) exactly four, (b) at least four, and (c) less than four.
What is the maximum likelihood estimate of theta? d. What is an approximate standard error of the maximum likelihood estimate?
If the politician is correct, what is the chance that you would observe 9 or fewer accidents involving a teenage driver?
to test h0 versus h2 a simple random sample of size n 15 is obtained from a population that is known to be normally
The sample standard deviation of the first set of strengths was 8.2 ksi, the second set's S value was 9.8 ksi, and the S value for the 25 differences in strengths was 3.3 ksi.
according to the empirical rule if the data form a bell shaped normal distribution what percent of the observations
What percent of the SAT verbal scores are less than 650 and if 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575?
can you reject the auto maker's claim that the mean gas mileage of its sports utility vehicle is 20 miles per gallon? Assume the population is normally distributed.
Suppose your instructor randomly surveyed his or her performance (i.e., students "graded" the teacher) over many years (assume an 'infinite' population). The frequency of ratings were as follows:
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