Proof by Contradiction

To disprove a theorem or a statement all you need is one counter example. Unfortunately, no number of examples supporting the theorem is sufficient to prove its correctness. You can never really prove the proposition that “All swans are white” even if you have only seen white swans in your entire life. But you can…

Regression Analysis

Given below are the Math and Statistics scores of five randomly selected tenth grade students in 2012. You are the Math teacher in the school. In 2013 the school principal asks you the following question. If a student scores 90 in math how much would he score in statistics? How would you solve this problem.…

Regression to the mean

Consider the following statement made up by Daniel Kahneman author of Thinking Fast and Slow Depressed children treated with an energy drink improve significantly over a three-month period. What do you infer from this? Most likely you will think that the energy drink improved the depression among children. But it could also be that children…

Central Limit Theorem

The core concept of Central Limit Theorem is that a large, properly drawn sample will resemble the population from which it is drawn. This is a powerful concept in statistics. In the book Naked Statistics At times, statistics seems like magic. We are able to draw sweeping and powerful conclusions from relatively little data. Somehow we…

Correlation and Causation

Correlation measures the degree to which two phenomena are related to one another. For example, there is a correlation between summer temperatures and ice cream sales. When one goes up, so does the other. Two variables are said to be Positively correlated – When a change in one is associated with the change in another in the same direction.…

Bayes Theorem

I came across the problem given below in Thinking Fast and Slow. A cab was involved in a hit-and-run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data 85% of the cabs in the city are Green and 15% are Blue. A witness…

Law of Small Numbers

An Urn has 100 Marbles; 50 red and 50 white. You draw 4 marbles(with replacement). What is the probability of all the 4 marbles, have the same color. Case 1: All Red P(1 Red Ball) = 50/100 = 1/2 = 0.5 P(4 Red Ball) = 0.5 ^ 4 = 0.0625 Case 2: All White P(1…