Exercises for Tue Aug 25: ¡­

Exercises for Tue Aug 25:

Extra 1: Consider Z =(X1 + ... + Xk - k mu)/(sqrt(k)*sigma), where the X's are i.i.d. uniform (0,1), with mu = 1/2 and sigma = sqrt(1/12). Simulate 10^4 such variables for k = 1, and give a histogram; then similarly 10^4 values for k = 2, with a histogram; etc., for k up to say 10. Comment on what is being shown by these histograms.

Extra 2: Simulate 10^4 random variables Xi from the unit exponential distribution, and compute the sequence Z1, Z2, ..., where Zn is the mean of the n first (Xi - mean(Xn))^3. Plot them, and comment on what you find.

Then, from ELL's exercises for Ch 2: Nos. 1.1 to 1.5; 1.8, 1.9.