This is part of a free course in Undergraduate Probability: https://www.math.uci.edu/~rvershyn/teaching/ugp/ugp.html
0:00 Recall the definition of a random variable X,
1:49 its distribution of X,
2:16 and the probability mass function of X.
3:32 Expectation is a single value that "best describes" X.
4:10 To define expectation, let's consider a motivating example.
7:14 A formal definition of the expected value
8:01 If all values are equally likely, expectation reduces to arithmetic mean,
8:49 and in general it is a weighted average.
9:06 In physics, it corresponds to the center of mass
9:30 Example: the expected number of heads in 3 coin flips is 1.5
10:35 Example: the expected winnings in a lottery
