Unformatted text preview: X ? c) Find an expression for ( 1) P X = . d) Explain why and how to use a binomial probability to approximate ( 1) P X = . 3. Suppose, in a Poisson process, there are 3 events on average per hour. a) What is the probability of exactly 2 events in the first hour? b) What is the probability of at least 2 events in the second hour? c) What is the probability of exactly 2 events in the first hour and at least 2 events in the second hour? d) What is the probability of exactly 2 events in the first hour or at least 2 events in the second hour? e) Find the probability ( ) p t of exactly one event in a period of t hours. f) Find lim ( ) / t p t t ! and provide an interpretation of this limit. 4. In question 3, a) If W is the time until the first event, find ( 1) P W ! . b) If V is the time until the second event, find ( 2) P V ! ....
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 Spring '10
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 Probability, Probability theory, random variables Exercises

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