Probability – S18.3 Hoeffding’s Inequality
In this segment we look into the probability that the sum of n independent identically distributed random variables takes an abnormally large value. We will get an upper bound on this quantity, which is known as Hoeffding’s inequality. This is an upper bound that applies to a special case, although the method actually generalizes. Here …
Probability – S18.2 Jensen’s Inequality
Let X be a random variable, and let g be a function. We know that if g is linear, then the expected value of the function is the same as that linear function of the expected value. On the other hand, we know that when g is nonlinear, in general, these two quantities will not …
Probability – S18.1 Convergence in Probability of the Sum of Two Random Variables
This is a rather theoretical exercise that has two purposes. One is to verify that the notion of convergence in probability is quite natural and that it has properties similar to the notion of convergence of sequences. And the second purpose is to get a little bit of practice with the formal definition of convergence …
Probability – S18.1 Convergence in Probability of the Sum of Two Random Variables Read More »
Probability – L18.8 Related Topics
The purpose of this segment is to give you a little bit of the bigger picture. We did discuss some inequalities, we did discuss convergence of the sample mean– that’s the weak law of large numbers– and we did discuss a particular notion of convergence of random variables, convergence in probability. How far can we …