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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 define 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).

ANSWER

p : 20-10-0.83 lday 21 25 $21,25 pri 25): e- (083)

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