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Question 1 (20 points, Poisson or not Poisson): Monthly Notices of the Royal Astronomical Society published...

Question 1 (20 points, Poisson or not Poisson): Monthly Notices of the Royal Astronomical Society published that a total of 20 kg asteroids hits the earth per day. (a) (5 Pts.) By using Poisson distribution, determine the probability of getting 5 kg of asteroids in 4 hours? (b) (5 Pts.) Determine the probability in Part (a) by using an appropriate continuous distribution. (c) (5 Pts.) If we de ne random variable X as the time required for 0.5 kg of asteroids hitting the earth, determine the PDF of X. (d) (5 Pts.) Now determine the probability in Part (a) by using the PDF you determined in Part (c).

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