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Chapter 4: Q. 4.33 (page 172)
Repeat Theoretical Exercise 4.32, this time assuming that withdrawn chips are not replaced before the next selection.
Probability mass function does not exist
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In Problem for if the coin is assumed fair, what are the probabilities associated with the values that X can take on?
Four independent flips of a fair coin are made. Let denote the number of heads obtained. Plot the probability mass function of the random variable .
An interviewer is given a list of people she can interview. If the interviewer needs to interview 5 people, and if each person (independently) agrees to be interviewed with probability 2 3 , what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of
(a) 5 people and
(b) 8 people? For part (b), what is the probability that the interviewer will speak to exactly
(c) 6 people and
(d) 7 people on the list?
A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective. Find the expected number of defective items in the sample.
The number of times that a person contracts a cold in a given year is a Poisson random variable with parameter . Suppose that a new wonder drug (based on large quantities of vitamin ) has just been marketed that reduces the Poisson parameter to for percent of the population. For the other percent of the population, the drug has no appreciable effect on colds. If an individual tries the drug for a year and has colds in that time, how likely is it that the drug is beneficial for him or her?
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