What is the probability that the number of cars N(1) that arrive in an hour is less than 4 • Find the time k such that the probability of time between two successive arrivals T exceeding k is 0.2 (Hint: Note that both are different random variable and will have different distributions.)
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Problem 1
A car repair shop experiences cars arriving for repairs as a Poisson process with an average rate of 4 cars per hour.
• What is the probability that the number of cars N(1) that arrive in an hour is less than 4
• Find the time k such that the probability of time between two successive arrivals T exceeding k is 0.2
(Hint: Note that both are different random variable and will have different distributions.)
Problem 2
Let X be a random variable following a gamma distribution with shape param- eter a = 3 and scale parameter ẞ = 2, denoted as X ~ Gamma(a, B).
• Compute the probability Pr(1 < x <5)
• Here X also follows a x2 distribution (special case of Gamma distribution). Find v. Then, write down its probability density
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