FULL WORKING. ONLY ANSWER QUESTION 1 AND QUESTION 3. question 2 isONLYreference for question 3:

QUESTION 1:

In order to earn enough to pay yourfirmsdebt this year, you will need to be awarded at least 2 contracts. This is not usually aproblem,since the yearly average is 5.1 contracts. you may assume a Poisson distribution.

a) find the probability that you will not earn enough to pay yourfirmsdebt this year

b)find the probability that you will be awarded exactly 3 contracts

QUESTION 2:

A Tv system is expected to last for 50,000 hours before failure. Assume an exponential distribution for the time until failure.

a) is the distribution skewed or symmetric?

b) what is the standard deviation of the length of time until failure?

c) the system has been working continuously for the past 8,500 hours and is still on. what is the expected time from now until failure? (be careful!)

QUESTION 3:

Assuming the appropriate probability distribution for the situation described in the preceding problem:

a) find the probability that the system will last 100,000 hours or more (twice the average lifetime)

b) the system is guaranteed to last at least 5,000 hours. What percentage of production is expected to fail during the guarantee period?