SHOW ALL WORK. n=36

1. Assuming X has a Poisson distribution, what is the estimated parameter? Get the 95% CI for your parameter(10 points)
2. Give an estimate of the probability that there are at least 8 occurrences in a randomly given month(5 points)
3. Give an estimate of the probability that your sample mean occurrence is at least 8(5 points)
4. Assuming Y has an exponential distribution, what is the estimated parameter? Get the 95% CI for your parameter(10 points)
5. Give an estimate of the probability that the time till first occurrence in a given month is more than 4 days(5 points)
6. Give an estimate of the probability that your sample mean time till first occurrence is more than 4 days(5 points)
7. Give an estimate of the probability that 2 occurrences happen within 10 days(5 points)
8. If you are asked to work on data in 2 consecutive years, can you construct CI the same way as you did in 3 & 4?(5 points)
9. We assumed a Poisson distribution in 3. Is this a reasonable assumption? Explain why you think it is or it is not.(5 points)
10. Theoretically what is the relationship between random variable X and Y if assuming X is a Poisson process? Does the data support this theoretical relationship? If not, any possible reasons why?(5 points)

X Y (Jan 2004 - Dec 2006)

8 9

8 6

9 5

12 2

7 7

9 4

12 2

10 6

5 3

15 1

12 5

15 3

6 7

11 4

11 4

10 1

11 6

14 1

10 1

14 3

14 2

11 5

8 4

15 9

10 6

9 3

15 3

17 7

12 4

15 2

11 7

16 2

14 1

12 6

13 3

23 1