1 post published by Dan Ma during March 2010| A Blog on Probability and Statistics
There are two celebrated problems in probability that originated from the French professional gambler Chevalier de Méré (1607-1684). The problems were solved jointly by Blaise Pascal (1623-1662) an…| A Blog on Probability and Statistics
2 posts published by Dan Ma during November 2016| A Blog on Probability and Statistics
The occupancy problem in probability theory is about the problem of randomly assigning a set of balls into a group of cells. In randomly placing $latex k$ balls into $latex n$ cells, what is the pr…| A Blog on Probability and Statistics
An important part of probability theory concerns with the sums of independent random variables. In many situations, the number of terms in the independent sum is itself a random variable. Introduct…| A Blog on Probability and Statistics
When a gambler consistently loses large sum of money, what can he or she do? When one particular gambler, Chevalier de Méré (1607-1684), was losing a big fortune, he called a “mathematical he…| A Blog on Probability and Statistics
This is a short illustration on the problem of points. Here’s a description of the famous problem of points. Two players play a game of chance with the agreement that each player puts up equal stak…| A Blog on Probability and Statistics
This post highlights certain basic probability problems that are quite easy to do using the concept of Markov chains. Some of these problems are easy to state but may be calculation intensive (if n…| A Blog on Probability and Statistics
Suppose that a patient is to be screened for a certain disease or medical condition. There are two important questions at the outset. How accurate is the screen or test? For example, at the outset,…| A Blog on Probability and Statistics
A student in a probability course may have evaluated an integral such as the following: $latex \displaystyle \int_0^\infty \displaystyle t^{x-1} \ e^{-t} \ dt$ Plug in a value for $latex x$ and eva…| A Blog on Probability and Statistics
The previous post is on the Monty Hall Problem. This post adds to the discussion by looking at three pieces from New York Times. Anyone who is not familiar with the problem should read the previous…| A Blog on Probability and Statistics
The post discusses the Monty Hall problem, a brain teaser and a classic problem in probability. The following 5 pictures describe the problem. Several simple solutions are presented. ______________…| A Blog on Probability and Statistics
What better way to celebrate Pi Day than to have a blog post on the digits of $latex \pi$! Giving pi as tips The number $latex \pi$ is the ratio of the circumference of a circle to its diameter. It…| A Blog on Probability and Statistics
Consider this random experiment. You ask people (one at a time) of their birthdays (month and day only). The process continues until there is a repeat in the series of birthdays, in other words, un…| A Blog on Probability and Statistics
This post discusses the coupon collector problem, a classical problem in probability. ___________________________________________________________________________ The Coupon Collector Problem The pr…| A Blog on Probability and Statistics
In this post, we discusses an example in which you are given a password (every character of it) and yet it is still very hard (or even impossible) to crack. Anyone who understands this example has …| A Blog on Probability and Statistics
This post discusses the problem of the gambler’s ruin. We start with a simple illustration. Two gamblers, A and B, are betting on the tosses of a fair coin. At the beginning of the game, play…| A Blog on Probability and Statistics