The word probability and chance are familiar to everyone. Many a time we come across statements like “It is possible that our school students may get state ranks in forthcoming public examination.
“Probably it may rain today”
Definition: The word chance, possible, probably, likely etc. convey some sense of uncertainty about the occurrence of some events. Our entire world is filled with uncertainty. We make decisions affected by uncertainty virtually every day. In order to think about and measure uncertainty, we turn to a branch of mathematics is called as probability.
Probability Distribution Definition-classical Definitions
Definition: If there are n exhaustive, likewise exclusive and in the same way likely outcomes of an experiment and m of them are favorable to an event A, and then the mathematical probability of A is defined as the ratio m/n.
Definition for random variable:
The outcomes of an experiment are represented by a random variable if these outcomes are numerical or if real numbers can be assigned to them. For example, in a die rolling experiment, the corresponding random variable is represented by the set of outcomes {1, 2, 3, 4, 5, 6} ; while in the coin tossing experiment the outcomes head (H) or tail (T) can be represented as a random variable by assuming 0 to T and 1 to H.
Types of Random variables:
(1) Discrete Random variable
(2) Continuous Random variable
Definition for Discrete Random Variable: If a random variable takes only a finite or a countable number of values, it is called a discrete random variable.
Example:
1. The number of heads obtained when two coins are tossed is a discrete random variable as X assumes the values 0, 1 or 2 which form a countable set.
2. Number of Aces when ten cards are drawn from a well shuffled pack of 52 cards.
Probability Distribution Definition-theoretical Distributions:
Theoretical probability distributions is classified into
1. Binomial Distribution
2. Poisson Distribution
3. Normal Distribution
4. Exponential Distribution
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