##### School: University of Illinois at Chicago

##### Department: Industrial Engineering

##### Course: Probability Stat for Engineer

##### Professor: Scott Reckinger

##### Term: Fall 2018

##### Tags: Statistics and Probability

##### Name: IE 342 Week 6 Notes

##### Description: These notes contain some important concepts like expected value of a random variable, and also variance of a random variable. There are detailed explanations for each section along with graphs and examples to make the concepts more clear.

##### Uploaded: 10/09/2018

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Unformatted text preview: ooitto Week 6 NOTES Expeche dation Expectation of a function of a Random variable ->let X be a distribution fc nordom variable with probability Let g(xbe a waniable X , then function expected of a condem value o gox) f(x) 66x) [ Discrete] 15 Mg(x+ - E[g(x)] = 90*) Fex) dx continuous - [* g(x) acts like another random wariable Example Random usest. I blomstrong neslakes R 50- Lets say that the pdf is Kon to be f 24, 3 0 % 2 KC1-x) 0.8 % X 1 FCX) = . OtherwiseFiod k such that f(x) is a valid pidif: fax. dx Area : bih => K2 Find the expected cussent. I value of xf2dx * C- 8 fux dx + xuli-x) dx= 4 .5 Find the expected value of ised up erp ZEET x2.50 .fcx) dx 50. xdx + 50x411-> dx 0-S is VARIANCE : special cose L a boue ax=18 u - fine sowammerd deviation of mean? x from its