Day 1 : Binomial

In probability theory and statistics, the Binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or_failure_ (with probability q=1-p.

🔔 Random Facts 🔔

Let X ~ Bin(n, p1) and Y ~ Bin(m, p2) be independent. Let T = (X/n) / (Y/m). Then log(T) is approximately normally distributed with mean log(p1/p2) and variance ((1/p1) − 1)/n + ((1/p2) − 1)/m. This result was proved by Katz et. al. in 1978 in their paper “Obtaining Confidence Intervals for the Risk Ratio in Cohort Studies”.