Assume that the Pb data in Box 3.2 are annual maximum EMCs for 1997 through 2005. Estimate the median, 90th, and 95th percentiles:

1) nonparametrically with Eq. 3.12, (3 pts)

2) assuming a normal distribution, and (3 pts)

3) assuming a lognormal distribution. (3 pts) Estimate the two-year, 10-year, and 25-year return period EMCs assuming:

4) a normal and (3 pts)

5) lognormal distribution. (3 pts)

6) What is the longest return-period EMC than can be estimated nonparametically? (3 pts)

(4) Is the Markov chain whose transition matrix whose transition matrix is 0 0.4 0.67 regular? (Yes or No) (5) Is the Markov chain whose transition matrix whose transition matrix is 0.2 0 0.8 0.6 0.4 0 regular? (Yes or No)For each of the following transition matrices, determine whether the Markov chain with that transition matrix is regular. (1) Is the Markov chain whose transition matrix whose transition matrix is 0 0.2 0.8 0 0 0.2 0.8 0 regular? (Yes or No) (2) Is the Markov chain whose transition matrix whose transition matrix is 1 0 0 0.5 0.5 regular? (Yes or No) (3) is the Markov chain whose transition matrix whose transition matrix is regular? (Yes or No) (4) Is the Markov chain whose transition matrix whose transition matrix is regular? (Yes or No)Let B and B' be two bases (in matrix form) for R". The following statements are true about the transition matrix from B' to B: (a) If B = I, then the transition matrix is B'-1. b If B = I, then the transition matrix is B'. (c) If B' = I, then the transition matrix is B-1. (d) If B' = I, then the transition matrix is B.Finding a Transition Matrix In Exercises 17-24, find the transition matrix from B to B'. 20. B = {(1, 1), (1, 0)}, B' = {(1, 0), (0, 1)} Finding Transition and Coordinate Matrices In Exercises 37-40, (a) find the transition matrix from B to B', (b) find the transition matrix from B' to B, (c) verify that the two transition matrices are inverses of each other, and (d) find the coordinate matrix [X]g, given the coordinate matrix [x]B- 38. B = {(2, -2), (6, 3)}, B' = {(1, 1), (32, 31)}, 2 [x ]B' =