.. title: Engineering Probability Class 9 Mon 2021-02-25 .. slug: class09 .. date: 2021-02-25 .. tags: class .. link: .. description: .. type: text .. has_math: true .. sectnum:: .. contents:: Table of contents:: .. Back test --------- Spring 2020 exam one, with or w/o solutions: https://wrf.ecse.rpi.edu/Teaching/probability-s2020/posts/class11-exam1.html https://wrf.ecse.rpi.edu/Teaching/probability-s2020/posts/class11-exam1-sol.html Note that the material is somewhat different each year. Exam one -------- #. The material will be up through Chapter 2. #. The test platform will be gradescope. #. The test will be in class time on Mon. #. Students with accommodations will start at 3 and run late. #. Students in China and similar places will have the option to write the test at 3am EST. #. If you are in China and want this, tell me where you are by tomorrow. 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? Chapter 3 Discrete Random Variables ----------------------------------- (Today we did the text through p 109.) #. This chapter covers **Discrete** (finite or countably infinite) r.v.. This contrasts to continuous, to be covered later. #. Discrete r.v.s we've seen so far: #. uniform: M events 0...M-1 with equal probs #. bernoulli: events: 0 w.p. q=(1-p) or 1 w.p. p #. binomial: # heads in n bernoulli events #. geometric: # trials until success, each trial has probability p. #. 3.1.1 p107 Expected value of a *function* of a r.v. #. Z=g(X) #. E[Z] = E[g(x)] = :math:`\sum_k g(x_k) p_X(x_k)` #. Example 3.17 p107 square law device #. :math:`E[a g(X)+b h(X)+c] = a E[g(X)] + b E[h(x)] + c` #. Example 3.18 Square law device continued #. Example 3.19 Multiplexor discards packets #. Compute mean of a binomial distribution. #. Compute mean of a geometric distribution. #. 3.3.1, page 107: Operations on means: sums, scaling, functions Xkcd comic ---------- `Seashell `_