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# Solved paper 31980

) From a recent statistical analysis for the last fiveyears,. ) From a recent statistical analysis for the last fiveyears, on an average there are 4 (major) air accidents per month in the world. Let X be thenumber of air accidents occurred in a randomly selected month. It is known that X ~Poisson(l) approximately, where theintensity l 4 accidents (monthly averagenumber of accidents). Find the probability that there will be 4 or more air accidents (1) in a givenmonth of the next year; Hint: Therequired probability is P(X 4). Ans.(2) in 4 of thefirst 6 months of the next year; Hint: 1st 4th 5th 6th | | | | | | | 6C4 different ways to specify4 months p p p p 1-p 1-p EventDefine Y = # of months in the first 6 months of the next year inwhich 4 or more air accidents occur in a month . Y has a binomialdistribution. Compute P(Y = 4).Ans.(3) for the first time in the next year in June; Hint:Define Y = # ofmonths required to observe the first occurrence of the event A (i.e., 4 or moreair accidents occur in a month) (start from first month of next year). Noticethat if the first occurrence is in June, the event did not happen from January to May.In other words, the event in this problem is (X<4, X<4, X<4, X<4,X<4, X 4).Ans.(4) Compare the probabilities calculatedin (2) and (3), and why explain these probabilities are larger or smaller.Ans. ) From a recent statistical analysis for the last fiveyears,

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