ENEE 621/SPRING 2016

ESTIMATION AND DETECTION THEORY HOMEWORK # 1:

Please work out the ten (10) problems stated below – GS refers to the text: Geoffrey R. Grimmett and David R. Stirzaker, Probability and Random Processes, Oxford University Press, Oxford (UK), 2001. With this in mind, Exercise 1.2-2 (GS) refers to Exercise 2 for Section 1.2 of GS while Problem 1-31 (GS) refers to Problem 31 for Chapter 1 in GS.

Show work and explain reasoning. Three (3) problems, selected at random amongst these ten problems, will be marked.

1. Let ℙ be a probability measure on (Ω, F). For arbitrary events A and B in F, can you evaluate ℙ [AΔB] in terms of ℙ [A], ℙ [B] and ℙ [A ∩ B]? Explain.

2. Solve Exercise 1.2-2 (GS).

3. Solve Exercise 1.3-1 (GS).

4. As in Exercise 1.3-2 (GS), a fair coin is tossed repeatedly. Provide a description of the sample space of all possible outcomes, and of the assignment probability.

5. Solve Exercise 1.3-2 (GS).

6. Solve Exercise 1.3-6 (GS).

7. Solve Exercise 1.4-7 (GS).

8. Solve Exercise 1.5-4 (GS).

9. Solve Exercise 1.5-7 (GS).

10. Solve Problem 1-31 (GS).