probability sample space

The set of all possible outcomes of a random experiment is called the sample space, associated with the random experimen..

An experiment repeated under essentially homogeneous and similar conditions results in an outcome, which is unique or not unique but may be one of the several possible outcomes. When the result is unique then the experiment is called a deterministic experiment . Any experiment whose ..

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 h..

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..

>If A, B and C are mutually exclusive then Total Probability: P(A) = P(E 1 ) P(A|E 1 ) + P(E 2 ) P(A|E 2 )+ +P(E n ) P(A|E n ) Random variable: A real valued function 'X' defined on the sample space is called a random variable. Discrete random variable: A random variab..

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 ..

S= {1,2,3,4,5,6}] If the event is set of elements less than 2, then E = {1} is a simple event 1) Simple Event: If an event has one element of the sample space then it is called a simple or elementary eve..

Law of Total Probability: 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 S. Baye's Theorem: Let S be a sample space. If A 1 , A, A 3 ... A n are mutual..

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. d..