.. title: Engineering Probability Class 19 Thurs 2020-04-06 .. slug: class19 .. date: 2020-03-09 .. tags: class, exam .. link: .. description: .. type: text .. has_math: true .. sectnum:: .. contents:: Table of contents:: .. Exam 2 ------ is replaced by a normal class. Today ----- `Radke's Engineering Probability Lecture 18: Sums of random variables and laws of large numbers `_. `Notes <../files/radke/lec18.pdf>`_ . Mathematica ----------- Today I will also (try to) demonstrate using Mathematica for the sum of 2 and 4 uniform random variables. The pdf is a conditional, which is messy to work with by hand. Homework -------- I will put a new homework online, due in a week. Presentation ideas wanted ------------------------- If another of your profs is using a remote teaching technique that you like, tell me. I might try it. Watching lecture videos ----------------------- Following the suggestion of some ECSE people, I've been uploading videos from Webex to Mediasite. I'm going to try just posting the Webex link for you. It will save me a step, and solve the impending problem of Mediasite running out of space soon. Tell me how you like this. To watch before next class -------------------------- `Radke's Engineering Probability Lecture 19: The Central Limit Theorem `_. Min, max of 2 r.v. ------------------ #. Example 5.43, page 274. Chapter 6: Vector random variables, page 303- --------------------------------------------- #. Skip the starred sections. #. Examples: a. arrivals in a multiport switch, #. audio signal at different times. #. pmf, cdf, marginal pmf and cdf are obvious. #. conditional pmf has a nice chaining rule. #. For continuous random variables, the pdf, cdf, conditional pdf etc are all obvious. #. Independence is obvious. #. Work out example 6.5, page 306. The input ports are a distraction. This problem reduces to a multinomial probability where N is itself a random variable.