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Please explain in details, and I don't want answers copied from other WEBSITES ANSWERS . Thanks! #1 The number of accidents in a nasty intersection

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Please explain in details, and I don't want answers copied from other WEBSITES ANSWERS. Thanks!

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The number of accidents in a nasty intersection has a Poisson distribu- tion with mean 15 per year. Find the probability that there will be at least one accident during a given month.X and Y are independent Poisson variables with means , and 12 respectively. Find the distribution of X + Y. (Hint: Find the MGF of X + Y.)A student takes an infinitely long multiple choice exam. Each question has one correct and four incorrect answers. The student fills in the answers at random. Calculate the probability that the student would have marked at most two correct answers before marking the eighth incorrect

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