Suppose the average number of days between car accidents at a specific intersection is 64 days, and follows an exponential distribution
a) what is the probability that there will be there will be three months between accidents (assume 30-day months)
P(time between accidents=90days)
$\int_1^{90} λe^{- λT} dT = [-e^{- λT}]_1^{90}$
$-e^{-(64)(90)} = 0$ and $-e^{-(64)(1)} = -1.604X10^{-28 } $
$= 1.604X10^{-28}$
b) if an accident occurs at the beginning of a 30 day month, calculate the probability that another accident will occur in the same month
c) what is the variance of the times between accidents?
I'm not sure if I did a) right because for some reason i keep getting the same answer for b) even if i plug in a different number. Please help