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In each of the summer months (June, July, August), the number of accidents per months at a busy intersection is Poisson distributed with mean 1.5 accidents/month. For all other months, the number of accidents is Poisson distributed with mean 0.5 accidents/month. 7. a) (3 pts) First, let Y an, YFeb, YMar,... be the number of accidents occurring in the months of January, February, March, etc. Define a variable A- the total number of accidents occurring in the second half of the year (read: July through December) at this intersection. Write an expression for A in terms of Jan Feb Mar b) (5 pts) Second, using properties proven in class andlor listed on the Properties from Section 65 Handout, find the distribution of A. CLEARLY TELL ME which property or properties you use from that sheet. .Show the work done with said property or properties to find the distribution. . Give the name of the distribution and its parameters. c) (3 pts) Third, find the probability that exactly three accidents occurred at this intersection in the last half of the year

Properties from SECTION 6.5 (we did in class or you did them on homework or on a worksheet)/ 1. Ifx ~ N(μ, 2. IfZ No, I), then x(l) 3· IfY ~ Gamma(c=-B) and W =-then w~ σ), then Z =_ ~ N(0, 1) 21. r. 7. IfY, ~ Poisson(S)(一_n, ing) and U=y., then U-Poisson(Σλǐ). 8. IfY, Gamma(a, β)(H, ,n,in and U: Y, then U, Gamma(Σαβ). (Note: all same β) 9. IfY, Exponential( )(i , n iid) and U=< Y then Ụ ~ Gamma( α = n, β) (Note: all same β) 10. IfY Binomial P) -1, m, ind and U- V, then U- Binomialn, p) Note: all same p) I1. IFY, and Y, are independent txswith mgtmy t) andl myz (t), then Some other important properties to remember:

math   Statistics-And-Probability   
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