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Engineering Probability Class 9 Mon 2021-02-25

Source

2 Exam one

  1. The material will be up through Chapter 2.

  2. The test platform will be gradescope.

  3. The test will be in class time on Mon.

  4. Students with accommodations will start at 3 and run late.

  5. Students in China and similar places will have the option to write the test at 3am EST.

  6. If you are in China and want this, tell me where you are by tomorrow.

3 Probability in the real world - enrichment

Oct. 5, 1960: The moon tricks a radar.

Where would YOU make the tradeoff between type I and type II errors?

4 Chapter 3 Discrete Random Variables

(Today we did the text through p 109.)

  1. This chapter covers Discrete (finite or countably infinite) r.v.. This contrasts to continuous, to be covered later.

  2. Discrete r.v.s we've seen so far:

    1. uniform: M events 0...M-1 with equal probs

    2. bernoulli: events: 0 w.p. q=(1-p) or 1 w.p. p

    3. binomial: # heads in n bernoulli events

    4. geometric: # trials until success, each trial has probability p.

  3. 3.1.1 p107 Expected value of a function of a r.v.

    1. Z=g(X)

    2. E[Z] = E[g(x)] = \(\sum_k g(x_k) p_X(x_k)\)

  4. Example 3.17 p107 square law device

  5. \(E[a g(X)+b h(X)+c] = a E[g(X)] + b E[h(x)] + c\)

  6. Example 3.18 Square law device continued

  7. Example 3.19 Multiplexor discards packets

  8. Compute mean of a binomial distribution.

  9. Compute mean of a geometric distribution.

  10. 3.3.1, page 107: Operations on means: sums, scaling, functions