Stat 449: Homeworks

Homework rules: You are allowed and are enouraged to discuss some points of the problems with another student in the class.
However you must write each problem on your own.

All the homework numbers refer to problem numbers in the text "Probability and Random Processes" by G.R. Grimmet and D.R. Stirzaker (Oxford University Press, 2001.)

  • Hw 1 - from  Sec 3.4: 1, 2;   Sec 3.11: 37;  Sec 4.14: 18;  Sec 5.1: 6, 8

  • Hw 2 - 1) show that if X is a non-negative discrete random variable then its G(s) is a non-decreasing function on [0,1];   2) if the offspring distribution is 0 or 2 with probability 1/2 calculate G_n(s) and P(Z_n=0);   from Sec 5.4: 1, 3;   Sec 5.3: 1;

  • Hw 3 - 1) show that if X is conts and f(x)=f(-x) then the characteristic function of X is real valued for all t, and give one example of real valued char.ftion.;   from Chapter 5.7: 7;   5.8: 1 (i)-(iv), 5 (a)-(b), 11;   5.9: 3;

  • Hw 4 from Chapter 7.2: 1, 2, 7;   7.3: 3 (a)-(b), 13;   7.4: 1

  • Hw 5 from Chapter 7.5: 2;   7.7: 3;   7.8: 1,3;   12.5: 4, 6