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 expectation
0:52 and linearity property.
1:13 Example: compute the expected number of sick people in a group
2:24 by decomposing it into a sum of indicators
3:31 Group testing problem
8:49 solved
9:10 The answer can be simplified using Bernoulli inequality
9:44 Optimize the size of the group k
10:30 and obtain a bound on the optimal expected number of tests.
11:34 Iterating, we can do multistage group testing
12:15 which yields even more savings
