The time between accidents on a stretch of the Pennsylvania Turnpike has the pdf

Question

The time between accidents on a stretch of the Pennsylvania Turnpike has the pdf f(x) = 2e-2x for x>0 (=0 otherwise) and the times between accidents are independent of one another. Let Y = the longest period of time this stretch of highway will go between accidents before there are 11 accidents total. The pdf of Y is then given by: g(y) = 22e-20y for y>0 (0 otherwise) O gly) 22(1-e 2y)10 e 2y for y 0 (0 otherwise) O g(y) = 2e-2(y-x) for y>x (0 otherwise) O g(y) = 2e-2y for y:0 (0 otherwise)

Explanation / Answer

The PDF is provided in the question.

We need to find the CDF,which is to be calculated in the intervals (-, 0), (0,x) and (x,).

Which is F(x)= 1- e{-2x}, x>0

Y be the longest period of accidents and N=11

The PDF of Y is givn by,

g(y)=n{F(Y)}n-1 f(y) = 11{1- e-2y}10 (2 e-2y)

= 22(1-e-2y)10 e-2y

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