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1. Falling stars are assumed to follow a homogeneous Poisson process with rate λ = 4 per hour. (a) Write down the distri
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1. Falling stars are assumed to follow a homogeneous Poisson process with rate λ = 4 per hour. (a) Write down the distri
1. Falling stars are assumed to follow a homogeneous Poisson process with rate λ = 4 per hour. (a) Write down the distribution of the number of falling stars per six-hour time interval. (b) What is the probability that at least one falling star is observed in a one-hour time interval? [3] (c) Calculate the probability that the time until the next falling star is greater than 30 minutes. [4] (d) Write down the distribution of the time until three more falling stars are observed. [3] (e) What is the expected number of falling stars observed in a 12 hour period? [3]
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