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Monty Hall problem: A apparently counter-intuitive problem in the probability which gets its name from the TV game show, 'Let's Make a Deal' hosted by the Monty Hall. On show a participant is shown three doors behind one of which is the valuable prize and behind the other two are the booby prizes. The participant selects the door and then, before the opted door is opened, the host opens one the two left behind doors to reveal one of the booby prizes. The participant is asked if he/she would like to stay with originally selected door or switch to the other, as yet, unopened door. Number of people think that the switching doors makes no difference to the probability of winning the valuable prize but several people are wrong because switching doubles this probability from a third to two thirds.
An oil company is considering whether or not to bid for an offshore drilling contract. If they bid, the value would be $600m with a 65% chance of gaining the contract. The company
Cluster analysis : A set of methods or techniques for constructing a sensible and informative classi?cation of an initially unclassi?ed set of data, using variable values observed
Build-Rite construction has received favorable publicity from guest appearances on a public TV home improvement program. Public TV programming decisions seem to be unpredictable, s
Asymmetric proximity matrices : Proximity matrices in which the non-diagonal elements, in the ith row and jth column and the jth row and ith column, are not essentially equal. Exam
Locally weighted regression is the method of regression analysis in which the polynomials of degree one (linear) or two (quadratic) are used to approximate regression function in
Lagrange Multiplier (LM) test The Null Hypothesis - H0: There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1: There is heteroscedasticity i.e. β 1
Matching distribution is a probability distribution which arises in the following manner. Suppose that the set of n subjects, numbered 1; . . . ; n respectively, are arranged in
Likelihood is the probability of a set of observations provided the value of some parameter or the set of parameters. For instance, the likelihood of the random sample of n observ
The equation linking the height and weight of the children between the ages of 5 and 13 and given as follows here w is the mean weight in kilograms and h the mean height in
A theorem which shows that any counting process may be uniquely decomposed as the sum of a martingale and a predictable, right-continous process called the compensator, assuming ce
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