astonky Posted September 13, 2017 Report Share Posted September 13, 2017 Hi, Could anyone please explain how to solve this type of question: In a ski resort, the probability of more than 3 accidents in any day at the weekend (Saturday and Sunday) is 0.24. Assuming a Poisson model, 1) Calculate the mean number of accidents per day at the weekend (Saturday and Sunday) I got to the point that P(x>3) =0.24 and P(x<3 or x=3) = 0.76. How do I continue from here? I also know that the answer is 2.49. 2) Calculate the probabilit that, in the four weekends in February, there will be more than 5 accidents during at least two of the weekends. I am completely lost as to how to approach this question. Any help (with clear explanations) is much appreciated. Thanks! Reply Link to post Share on other sites More sharing options...
kw0573 Posted September 14, 2017 Report Share Posted September 14, 2017 (edited) 1. From the formula for Poisson distribution, you should solve via calculator that . Note in calculator you can just directly plot the distribution. Eg. y = poissoncdf (x, 3) or whatever the syntax is and intersection with y = 0.76. 2. I think they mean in each of at least 2 weekends, at least 5 accidents/weekend. Because it's entire weekend, double expected value to 2.49 * 2 = 4.98. Define a new poisson distribution Y ~ Po(4.98) and find 1 - P(Y=5) - P(Y=4) - P(Y = 3) - ... - P(Y=0) and say that's some probability p Define a binomial distribution W ~ B(4, p) Question ask for P(W = 2) + P(W = 3) + P(W = 4). Hope that helps! Edited September 14, 2017 by kw0573 Reply Link to post Share on other sites More sharing options...
astonky Posted September 17, 2017 Author Report Share Posted September 17, 2017 Ok thank you very much, I now managed to solve part 1. For part 2 I am slightly confused about why you need both the poisson and the binomial distribution. Would you care to explain that further? Reply Link to post Share on other sites More sharing options...
kw0573 Posted September 17, 2017 Report Share Posted September 17, 2017 2. The question asks for P(In at least 2 weekends, each weekend has at least 5 accidents). Poisson distribution is used when the number of favorable events can theoretically go up to infinity. Binomial distribution when the number of favorable events is bounded. Hence we first use poisson to calculate P(at least 5 accidents / weekend), as there can be as many accidents as possible in a weekend. Then we use binomial to calculate P(such weekends / month) since the number of weekends is limited to 4. 1 Reply Link to post Share on other sites More sharing options...
astonky Posted September 17, 2017 Author Report Share Posted September 17, 2017 Ok, thank you so much for your help. Reply Link to post Share on other sites More sharing options...
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