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Chapter 6: Q.401 (page 401)
Suppose you roll a pair of fair, six-sided dice until you get doubles. Let T = the number of rolls it takes. Show that T is a geometric random variable (check the BITS)
All of the prerequisites for a geometric random variable are met. is a geometric random variable as a result.
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To introduce her class to binomial distributions, Mrs. Desai gives a -item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class.
Let the number of Patti's correct guesses.
To get a passing score on the quiz, a student must guess correctly at least times. Would you be surprised if Patti earned a passing score? Compute an appropriate probability to support your answer.
Friends How many close friends do you have? An opinion poll asks this question of an SRS of adults. Suppose that the number of close friends adults claim to have varies from person to person with mean and standard deviation . We will see later that in repeated random samples of size 1100, the mean response x will vary according to the Normal distribution with mean and standard deviation . What is role="math" localid="1649504967961" , the probability that the sample result x estimates the population truth to within ?
77. Blood types Refer to Exercise 75. How surprising would it be to get more than adults with type blood in the sample? Calculate an appropriate probability to support your answer.
Exercises 47 and 48 refer to the following setting. Two independent random variables and have the probability distributions, means, and standard deviations shown.
48. Difference Let the random variable .
(a) Find all possible values of D. Compute the probability that takes each of these values. Summarize the probability distribution of in a table.
(b) Show that the mean of is equal to.
(c) Confirm that the variance of is equal to .Find all possible values of . Compute the probability that takes each of these values. Summarize the probability distribution of in a table.
Checking for survey errors One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About % of American adults identify themselves as black. Suppose we take an SRS of American adults and let be the number of blacks in the sample.
(a) Show that is approximately a binomial random variable.
(b) Check the conditions for using a Normal approximation in this setting.
(c) Use the Normal approximation to 铿乶d the probability that the sample will contain between and blacks. Show your work.
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