The Florida DoT (Dept. of Transportation) keeps statistics on the Turnpike. The

Question

The Florida DoT (Dept. of Transportation) keeps statistics on the Turnpike. The Turnpike is divided by mile markers, the n^th mile being the one form marker n - 1 to n (e.g. the first mile is from the beginning, mile marker 0. to mile maker 1). Assume for this problem that no stretch and no time of day is more dangerous than any other. Let V be the mile at which the first accident of the day happens How is V distributed? (That is, what is the name of V's distribution?) Briefly, why? Let W be the first (i.e. smallest) mile at which any accident today happens. How is W distributed? Why? Let X be the number of accidents that happen today on the stretch from Miami to Orlando. How is X distributed? Why? Let Y be the time of day when the first accident of the day happens. How is Y distributed? Why? Let Z be the number of (posted) miles (i.e. one-mile stretches between markers) in which at least one accident happens. How is Z distributed? Why?

Explanation / Answer

a) V follows a geometric distribution because V be the mile at which the first accident occur that means V be a random variable needed to get first success.

b) W follows a Poisson distribution because it takes any accident in the first mile.

c) X also follows a Poisson distribtuion because number of accidents in between from Miami to Orlando is a example of poisson distributed.

d) Y is follows a exponential distribution

e) Z is follows binomial distribution.

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