The Monty Hall problem is a puzzle based on an American reality show ‘Lets Make a Deal’. It is a popular probability riddle that comes up when one is learning probability and statistics, since the first cut solution that comes to mind is often different from what we get by applying basic principles of probability…

# Category: Probability and Statistics

## Covariance and Correlation

Often in data science, we want to understand how one variable is related to another. These variables could be features for an ML model, or sometimes we might want to see how important afeature is in determining the target we are trying to predict. Both covariance and correlation can be used to measure the direction…

## Dartboard Paradox: Probability Density Function vs Probability

What is the Dartboard Paradox ? Assume your are throwing a dart at dartboard such that it hits somewhere on the dartboard. The dartboard paradox: The probability of hitting any specific point on the dartboard is zero. However the probability of hitting somewhere on the dartboard is 1. How can this be ? ( How…

## With the maximum likelihood estimate are we guaranteed to find a global Optima ?

Maximum likelihood estimate finds that value of parameters that maximize the likelihood. If the likelihood is strictly concave(or negative of likelihood is strictly convex), we are guaranteed to find a unique optimum. This is usually not the case and we end up finding a local optima. Hence, the Maximum likelihood estimate usually finds a local…

## What is stratified sampling and why is it important ?

Stratified sampling is a sampling method where population is divided into homogenous subgroups called strata and the right number of instances are sampled from each stratum. For further explanation visit here. This sampling is important to ensure that sampled dataset is representative of the entire population. To realise this point, consider an example of predicting…