STAT 425 W14

Homework

Homework 1 (due January 14).
For the data sets and distributions in Exercises 4.1 and 4.4 in the book:
(a) Compute the Kolmogorov distance between the empirical df and the proposed distribution in each of the problems.
(b) Does each of the data sets follow their suggested distribution?
(c) Provide a graphical assessment of the suggested distributions.
Remark: You can use the same answer to more than one part, if you wish.

Homework 2 (due January 21).
1. Consider the effect of estimating the exponential parameter on the level of the Kolmogorov-Smirnov test. You should use two diffeent true parameter values, and consider both the level of the test when using the cutoff 1.36, and what the cutoff should be to get a test on the 5% level.
2. Compare the distribution of annual global mean temperature between two of the data sets (which you get to pick) and two lengths.

Homework 3.

Homework 4 (due February 4).
1. Consider a (theoretical) roulette wheel divided into n sections that are alternating red and black. Assume that the arcs are all of equal length. Suppose that there are 32 of these alternating sections (we ignore the numbers and the zeros). Pearson (1900) reported data on runs from the casino in Monte Carlo in July of 1892. The run lengths were 1 (2462 plays), 2 (945), 3(333), 4(220), 5 (135), 6 (81), 7 (43), 8(30), 9 (12), 10(7), 11 (5) and 12 (1). Do these data agree with the theoretical distribution for run length for a fair roulette wheel? If not, can you explain the discrepancy (if you assume there are the same number of red anc black outcomes, can you apply the runs distribution?)?
2. The average total precipitation for Seattle (Sea-Tac airport) in December is 5.86 inches. In http://www.stat.washington.edu/peter/425/Data/Sea_precip_dec_15.txt are the observed daily Seattle precipitation values for December, 2015, in inches. Was 2015 an unusually wet December?

Homework 5 (due February 18).
(a) Let X have density f(x). Show that if F is the corresponding cdf, and if f is symmetric around the median m, then F(m-x)=1-F(m+x).
(b) Does the result in (a) suggest a way of checking for symmetry (Hint: think Q-Q-plot).
(c) Let F1(x)=1-F(-x).. Define the symmetry function Λ = (1-F1-1(F(x)))/2. Show that if f is symmetric around m, then Λ(x)=m
(d) Suggest a sample-based estmator of the symmetry function, and apply it to the Michelson data on the velocity of light in air.

Homework 6 (due February 25).
Steve Tew, Chief Executive Director of New Zealand Rugby, wants to know the effect of the rugby rule changes. In particular, the intention when the rules were changed was to make the play more continuous. The data are those we looked at in class on Feb 18. Your task is to respond to the request with a one-page memorandum, explaining in non-technical terms your answer to Mr. Tew's request. You may want to comment on the design of the study, which was commissioned by Mr. Tew's office. You may submit supporting technical materal, graphs etc., in an appendix of at most 5 pages.