MY MAIN PROBLEM IS FIGURING OUT WHAT DISCRETE DISTRIBUTION TO USE, BERNOULLI, BINOMIAL, DISCRETE UNIFORM, GEOMETRIC NEGATIVE BINOMIAL, OR POISSON. Every time I choose one, it's the incorrect one. Is there some way I can easily find out which one to use.
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3.40
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Let Y denote a random variable that has a geometric distribution, with a probability of success on any trial denoted by p.
a) Find P(Y>=2) if p=0.1
b) Find P(Y>4 | Y>2) for general p. Compare this result with the unconditional probability P(Y>=2).[This property is referred to as "lack of memory"]
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3.52
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The telephone lines coming into an airline reservation office are all occupied about 60% of the time.
a) if you are calling this office, what is the probability that you will complete your call on the first try?the second try? the third try?
b)If both you and a friend must complete separate calls to this reservation office, what is the probability that it will take a total of four tries for the two of you?
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3.58
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In the article cited in Exercise 3.57, the projected fatality rate for 1975 if the NMSL had not been in effect was 25 per 10^9 vehicle miles. Assume that these conditions had prevailed.
a) Find the probability that at most 15 fatalities occurred in a given block of 10^9 vehicle miles.
b) Find the probability that at least 20 fatalities occurred in a given block of 10^9 vehicle miles.
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3.66
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The number of bacteria colonies of a certain type in samples of polluted water has a Poisson distribution with a mean of two per cubic centimeter.
a)If four 1-cubic-centimeter samples of this water are independently selected, find the probability that at least one sample will contain one or more bacteria colonies.
b)How many 1-cubic-centimeter samples should be selected to establish a probability of approximately 0.95 of containing at least one bacteria colony?