The average number of claims submitted to an insurance firm is 12 per day. the amount of each claim follow exponential distribution with mean 100.

by defining the random variables and stating their distributions, find the probability that

(a) not more than 3 claims submitted arrived in a day;

(b) the waiting time between the 5th and the 6th claims is less than one hour;

(c) more than 400 claims submitted in 30 days;

(d) more than 3 days in which no claim is submitted in a week.

(e) the amount of the fifth claim is more than 200;

(f) the seventh claim is the forth claim that the amount of claim is more than 200.

(g) the total amount of five claims is more than 600.