Homeworks

• Problems related to the video of Session 6:

  • Problem 1: Let X be a "zero mean" random variable. Express its 5th order cumulant in terms of its moments.
  • Problem 2: kurt{X} means the 4th order cumulant of random variable X. Show that kurt{X} is a linear operator over independent random variables, that is, show that if X and Y are two independent random variables, then kurt{X+Y}=kurt{X}+kurt{Y}.
  • Due date: Friday 97/12/16.

• Problems related to the video of Session 5:

  • Manual part: Problems 2.15, 2.17, 2.19, 2.24 of Hyvarinen's book.
  • Computer programming part: Write a MATLAB program to compute the kurtosis of a random variable from its samples. Test you routine on U(0,1) and N(0,1) random variables, and compare the results with true values.
  • Due date of manual part: Tuesday 97/12/13.
  • Due date of programming part: Wednesday 97/12/14.

• Problems related to the video of Session 4:

  • Problems 2.2, 2.7, 2.9, 2.12 of Hyvarinen's book.
  • Due date: Sunday 97/12/11.