Exam #3 may be picked up outside 4114 EECS by 5 PM Friday
April 5-9, 1999

Problem Set #9 Hints:

Problem Set #6 Hints:

Problem Set #5 Hints:

Problem Set #4 Hints:
On Problem #1, do the problem using the given pm(M).
Then THINK: what property of that pm(M) was vital for UMP?
You do NOT have to PROVE your result--just EXPLAIN why it is true.

On Problem #4, use deterministic Cauchy-Schwarz:
(&int x(t)y(t)dt)2< (&int x(t)2dt)(&int y(t)2dt)

    Problem Set #3 Hints:
  1. Problem #1: Your answer should be simple to interpret.
  2. Problems #2,4: see back side of "Multichannel Cramer-Rao bound" handout.

In binary hypothesis testing, two different criteria
both lead to the same answer:
the likelihood ratio test:
  1. The likelihood ratio is LR(R)=pr|H1(R|H1) /pr|H0(R|H0).
  2. .
  3. MIN[Bayes risk=E[cost]] leads to the test LR(R) > < n
    where n=[p0(C10-C00)]/[p1 (C01-C11)]; these were defined on Jan. 8.
  4. Special case: Min[Pr[error]] (MEP) leads to n=p0/p1 (MAP).
  5. ROC (Receiver Operating Characteristic): Plot of PD vs. PF for all n.