Assignment 1: Section 5.3, Page 212, No.40 (For part a.: "probability distribution" means "probability mass function" in this case. Note that M can only be 0, 5, or 10, so there are three probabilities you need to figure out. For part b.: Write a Matlab code to empirically determine the p.m.f.'s of M=max(X1,...,Xn), for n=3, 5 and 8, turn in (i) some verbal description of the experiment, (ii) the Matlab code and (iii) some graphical outputs. For the case of n=3, make sure that your empirically determined p.m.f. agrees with the one you derive in Part a. of the problem.), Section 5.4, Page 218, No.52.

Due Date: Jan 21

Assignment 2: Section 6.1, No. 10, 15,  Computing assignment: Modify MeanEstimate.m to plot the pdf's (estimated using the histogram method described in pdfHistogram.m) of (i) the20%-trimmed mean and (ii) the sample mean of N=100 i.i.d. N(0,1) random variables. As in the code, generate K=10000 random samples for the two estimators --  recall that we think of the estimators themselves as a random variables also. Since for each estimator, you have 10000 observations, you can compute the sample variance of the two estimators. Do this, and compare the two sample variances. Which one is smaller ? Does the answer vary from simulation to simulation ? (It is possible that you do one set of simulation and observe that the sample variance of one estimator is smaller than that for the other estimator, but then if you do another simulation, you get a different conclusion.) Or somehow one estimator seems to always have a smaller (estimated) variance than the other ?

Run your program 10 times (i.e. perform 10 sets of simulations) and report what you see. Are your observations here consistent with what the MVUE theorem on Page 236 says?

Due Date: Jan 28

Assignment 3: Section 6.2: No. 22, 28. Section 7.1: No. 8, Section 7.2: No. 26.  Due Date: Feb. 4

Assignment 4: Section 8.1, No. 9, 10, 13. Section 8.2: 20, 21, 30. Section 8.3: 38, 40.  Due Date: WEDNESDAY. Feb. 20

Assignment 5: Sec. 8.4: 45, 46, 47. Section 9.1:  6. Section 9.2: 27. Section 9.3: 36. Due Date: MONDAY. Feb. 25

Assignment 6: Section 12.1: 10. Section 12.2: 16, 18. Section 12.3: 35, 36  Due Date: WEDNESDAY March 5.