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Cars arrive at a highway rest area according to a Poisson process with rate 9 per hour. Let X be the number of cars that

Cars arrive at a highway rest area according to a Poisson process with rate 9 per hour.

LetXbe the number of cars that arrive within an interval of duration 10 minutes. What is the standard deviation ofX?

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Cars arrive at a highway rest area according to a Poisson process with rate 9 per hour.

What is the probability that more than one car arrives within an interval of duration 3 minutes?

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A multiple choice quiz involves 30 questions, each with 5 alternative answers. Each question is awarded 10 marks if the correct answer is chosen, and 0 marks otherwise. Assume that one particular student answers the quiz by guessing, with a 1 in 5 chance of answering any single question correctly, independently of all other questions.

LetXbe the total number of marks obtained by this student.The mean and standard deviation ofXare:

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