
GAME THEORY
Game Theory is used for decision making under conflicting situation where there are one or more opponents(players). A player may be an individual, a group of individuals or an organisation. The models for which chess, poker, etc are the games which have the characteristics of a competition and are played according to definite rules(strategy). It…

Demography
The word demography is a combination of two Greek words “demos” and “graphos” meaning “human beings” and “writing/measurement” respectively. A Belgian Statistician “ACHILLE GUILLARD” was the first man to pronounce and designate the term “Demography” in the article “éléments de statistique humaine ou demographique comparee” (elements of human statistics or comparative demography). Definition: Duncan and…

2DRandom Variables
Let X and Y be two random variables defined on the same sample space S. Then the function (X,Y) that assigns a point in is called a two dimensional random variable. Examples: Joint CDF of (X,Y): The joint cdf of (X,Y) is defined as: Properties of CDF: Proof of Property 1: PROOF OF PROPERTY 2:…

Censoring Schemes
Many researchers consider survival data analysis to be merely the application of two conventional statistical methods to a special type of problem: parametric if the distribution of survival times is known to be normal and nonparametric if the distribution is unknown. This assumption would be true if the survival times of all the subjects were exact and…

Normal Distribution
A random variable X is said to follow a Normal Distribution with parameters and if it has a probability density function given by: A random variable X is said to follow a Normal Distribution with parameters and if it has a distribution function given by: First Four Moments: Skewness and Kurtosis Some Interesting Properties of…

Survival Analysis Notes (1)

Graphical Solution of LPP
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My Favourite Problems
Polya’s Urn At time 0, an urn contains 1 black and 1 white ball. At each time 1,2,3,…, a ball is chosen at random from the urn and is replaced together with a new ball of the same colour. Just after time n, there are therefore n+2 balls in the urn, of which Bn+1 are…

a football post?! — Xi’an’s Og
I am not interested in football, neither as a player (a primary school trauma when I was the last being picked!) or as a fan, contrary to my dad (who was a football referee in his youth) and my kids, but Gareth Roberts (University of Warwick) and Jeff Rosenthal wrote a paper on football draws […]…

JAM 2022 [ 41 50]
Let be a sequence of real numbers such that a1+5m=2 , a2+5m=3 , a3+5m=4 , a4+5m=5, a5+5m=6 , m=0,1,2, … . Then equals ____________________________ . It is evident that an is defined for all values of n=1,2,3,…. . And so

RANDOM NUMBER GENERATORS
What are random numbers? Imagine yourself picking up a card from a well shuffled full deck of cards. What could the card you picked be? The jack of spades, the king of diamonds, or the queen of hearts?? Well it could be the ace of clubs too or it could be any of the other…

SIMULATION
Simulation is a numerical technique for conducting experiments on a digital computer, which involves certain types of mathematical and logical models that describe the behavior of business or economic system or some component thereof over extended period of time. Simulation deals with both abstract and physical models. Some simulation with physical and abstract models might…

Monte Carlo Methods
A Monte Carlo method is a computational / numerical method that uses random numbers to compute / estimate a quantity of interest. The quantity of interests may be the mean of a random variable , functions of several means , distributions of random variables or high dimensional integrals. Basically, Monte Carlo methods may be grouped…

Operations Research: The ORIGIN
The origin of Operations Research can be traced back to the World WarIIperiod. During the time of war, the military management in England had calledupon a team of scientists to study the strategic and tactical problems related toair and land defence of the country. Since, the military resources were limited,it was upto these scientists to…

JAM 2022 [ 5160 ]
[Q No. 5160] Let be a random sample from a distribution, where are unknown. Let the observed values of be 9.8 and 1.44, respectively. If the likelihood ratio test is used to test the hypothesis then the pvalue of the test equals __________________ (round off to 3 decimals) We know that, Thus, the test statistic…