probability

Axiomatic approach to probability closely relates the theory of probability to set theory. Let S be the sample space of an experiment. Probability is a function, which associates a non-negative real number to every event A of the sample space denoted by P(A) satisfyin..

Random Variables and Probability Distributions - 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..

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 probability distribution ..

Multiplication Rule of Probability - We have already proved that if two events A and B from a sample S of a random experiment are mutually exclusive, then In this section, we examine whether such a rule exists, if ' ' is replaced by ' ' and '+' is replaced by 'x' in the above addition rul..

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..

We have already proved that if two events A and B from a sample S of a random experiment are mutually exclusive, then In this section, we examine whether such a rule exists, if ' ' is replaced by ' ' and '+' is replaced by 'x' in the above addition rule. If it does exist, what are the particular co..

If a trial is repeated N number of times under essential homogeneous ..

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 1 0 x is called a random variable, which can assume the v..

Let X be continuous random variable which can assume values in the interval [a,b]. A function f(x) on [a,b] is called the probability density function if ..

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