Event Detail

Event Type: 
Friday, October 6, 2017 - 10:00 to 11:00
Valley Library Room 3622

We state and prove a collection of concentration of measure inequalities as well as provide examples of these inequalities when applied to a Binomial random variable. Each example also includes a calculation of the sample size needed to establish P(|Y- EY| 1- ε for ε > 0. We then discuss an extension of the Chebyshev inequality from the typical second-moment formulation to higher ordered versions and apply this concept again to a Binomial random variable. We find that higher ordered moments offer notable improvements in the sample size necessary to ensure P(|Y- EY| 1- ε. We then establish an algorithm for determining E|Y- EY|2m for a Binomial random variable Y and m ∈ {1, 2, …}. Lastly, we state a conjecture that E|Y- EY|2m is maximized at p = 1/2 for all m when n is sufficiently large.