Unit · year 1
MU-106 · Probability I
Threads chance6 theorems
Events, random variables, expectation — reasoning quantitatively about uncertainty.
Theorems in this unit
T-034
The law of total probability
Probability of an event via a partition of the sample space.
T-035
Bayes' theorem
How to invert conditional probabilities.
T-036
Linearity of expectation
Expectation of a sum is the sum of expectations, dependence notwithstanding.
T-037
Markov's inequality
A tail bound from the mean alone for non-negative variables.
T-038
Chebyshev's inequality
A tail bound from the variance.
T-039
The weak law of large numbers
Sample means converge in probability to the expectation.