An expert says that the number of days before a new case discovered for a rare disease follow exponential distribution with mean 6.

(a) What is the variance of number of days before a new case?

(b) What is the probability that the number of days before a new case is less than 12?

Now consider that instead of rare disease, we are consider a pandemic where the number of days before a new case follow exponential distribution with mean 40. We would like to compute probability that the number days before a new case is less than 30.

(c) What is the Excel formula to compute the answer?