L05 11 Linearity Of Expectations Youtube Mit res.6 012 introduction to probability, spring 2018view the complete course: ocw.mit.edu res 6 012s18instructor: john tsitsiklislicense: creative. Watch more videos in the chapter 3: discrete random variables playlist here: playlist?list=pl qa2peruq6orivhloqmqjxamb b2nb85to learn mor.
Class 2 Video 1 Linearity Of Expectation Youtube Mit 6.042j mathematics for computer science, spring 2015view the complete course: ocw.mit.edu 6 042js15instructor: albert r. meyerlicense: creative co. Linearity of expectation is the property that the expected value of the sum of random variables is equal to the sum of their individual expected values, regardless of whether they are independent. the expected value of a random variable is essentially a weighted average of possible outcomes. we are often interested in the expected value of a sum of random variables. for example, suppose we are. 3.2: more on expectation slides (google drive)alex tsunvideo ( ) 3.2.1 linearity of expectation right now, the only way you’ve learned to compute expectation is by rst computing the pmf of a random variable p x(k) and using the formula e[x] = p k2 x k p x(k) which is just a weighted sum of the possible values of x. Now, by theorem 26.1, the expected value is e[x] = e[36w − 1] = 36e[w] − 1 = 36(1 38) − 1 = − 2 38, which matches what we got in lesson 22. the next result is even more useful. theorem 26.2 (linearity of expectation) let xx and yy be random variables. then, no matter what their joint distribution is, e[x y] = e[x] e[y].
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