probability

Events are said to be independent if the occurrence of one event does not affect the occurrence of others. If A and B are two independent events, then This is known as Multiplication Rule of Probability . The converse is also true, that is if two events A and B asso..

Introduction - From our earlier chapter we know that, in statistical experiments, if the events A and B are independent, then But suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional..

Random Variable and Probability Distribution - If is often very important to allocate a numerical value to an outcome of a random experiment. For example consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome : HH HT TH TT No. of heads (x) : 2 1 ..

A discrete random variable assumes each of its values with a certain probability, Let X be a discrete random variable which takes values x 1 , x 2 , x 3 ,x n where p i = P{X = x i } Then X : x 1 x 2 x 3 .. x n P(X): p 1 p 2 p 3 . . . . . p n is called the probabilityh..

Let S be a sample space associated with a given random experiment. A real valued function X which assigns to each w i S, a unique real number, X( w i ) = x i is called a random variable . Two types of random variables are 1. Continuous random variable, 2. discrete random varia..

It is often very important to allocate a numerical value to an outcome of a random experiment. For example, consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome HH HT TH TT No. of heads (x) 2 1 1 0 x is called a random variable, which can assume the valu..

If B 1 , B 2 , B 3 , .., B n are mutually exclusive and exhaustive events of the sample space S, then for any event A of ..

Summary - P {Occurrence of A given that B has occurred} = P (A|..

If A and B are any two events, the..