Q N 6 An engineer has observed that the gap times between ve

Q .N. 6) An engineer has observed that the gap times between vehicles passing a certain point on a highway have an exponential distribution with mean 10 seconds. Find the probability that the next gap observed will be no longer than one minute.

Solution

mean= 10 seconds= 10/60 min = 1/6 min

lambda= 1/mean = 6 min^-1

exponential distribution is given by P(x) = lambda*e^(-lambda*t) = 6*e^-6*t

cumlative distribution for exponential is P( X <= x) = 1- e^(-6*t)

Probability that next gap will be no longer than 1 min, P( x <= 1 ) = 1- e^(-6*1) = 0.997521