L06.7 Joint PMFs and the Expected Value Rule

MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: ocw.mit.edu/RE...
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
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[@tarunpahuja3443]

Think of each value of Y as a scenario. Under each scenario X can take value x with some probability. To find marginal probability, apply total law probability.

[@ZH59]

At 2:17, could someone explain to me why both P(Y=2) and P(X=1) are clearly greater than 0? But P(X=1 and Y = 2) is 0? Thank you!

[@youngjim7987]

why this cannot be true? Y can equal 2 and X can equal 1 but they cannot both equal to that number simultaneously

[@shardx191]

in this case they are not independent

[@tommymerelte4399]

excellent lecture mr

[@VuNguyen-pd1uq]

sadly, I can't understand very much. Why don't you demonstrate some specific example with real figure ?

[@AkashKumar-lr6hc]

awesome

[@nileshkharat236]

at 9:18 shouldn't it be double summation to be more accurate?

[@DeadPool-jt1ci]

No,you're not running the summation twice , you are running it once.Summing over PAIRS (x,y) such that g(x,y) = z. You get a single value z each time , and u sum over those z's. Essentially what i mean to say is that u sum over the OUTPUT of g(x,y) , not over the INPUT of g(x,y) which is X and Y , and then you would indeed need double summation.
An example , lets say g(x,y)= x+y , then for the pair (1,2) u have z=3.You add the 3 to your sum , not the 1 or the 2 to some double sum

[@nileshkharat236]

@@DeadPool-jt1ci got it. Thanks

[@tarunpahuja3443]

@@DeadPool-jt1ci We could do it with double summation too. Like For each value of x consider all value of y such that g(x,y) = z. This wont sum twice. Like its being done in Expectation.

[@samedy00]

The explanation of Dead Pool is not quite correct. You indeed sum over pairs (x,y) that give the same particular z, but do not sum over z's, since z is the variable at the left hand side and can not be the index of summation.

[@joshuac9142]

Very helpful!

[@avishshah2186]

3:15

[@brainstormingsharing1309]

👍👍👍👍👍👍👍👍

[@anas.said27]

the little russian accent made me sure that math and probability were made by russians lol ( foreigner student in russia )

[@Darwin_Somtoo]

🤧🤧

[@NaofumiShinomiya]

Thank you Kolmogorov! (Prof. Tsitsiklis is Greek btw)

[@charlesmendeslima1389]

2min

[@akashwaghmare3957]

it is not clear explained .