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Question 5. Suppose that the number of accidents in a city on a rainy day is...

Question 5. Suppose that the number of accidents in a city on a rainy day is a Poisson random variable with mean 8, on a cloudy day is a Poisson random variable with mean 5 and on a sunny day is a Poisson random variable with mean 2. If the probability that it will be rainy tomorrow is 0.4, the probability that it will be cloudy tomorrow is 0.3 and the probability that it will be sunny tomorrow is 0.3;

  1. (a) What is the expected number of accidents that will occur tomorrow?

  2. (b) What is the probability that the number of accidents that will occur tomorrow is at least two?

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