Note on Continuous Function

Definition of Continuous Function:

In study of probability, a Random Variable X is assumed as a continuous variable, if it can take all possible values within certain given limits. That is X is a continuous its values cannot be put in one to one associated with N.

A nonstop probability function f(x) is a function that satisfies the following properties:

• It is non-negative for all real X.
• The probability function of integral is one.
• Constant continuous probability functions are known as probability definition function (pdf).
• Since regular probability function are defined for uncountable number of
  points over an interval, the probability at a single point is always zero.

The probabilities are measured between intervals। That Is, the area under the curve stuck between two distinct points define the probability for that interval.This can also help us on how to simplify radicals.

P(a ≤ x ≤ b) = P(a ≤ X < b) = P(a < x ≤ b) = P(a < x < b)

Discrete Probability function is referred to as probability mass function.

Continuous probability functions are known as probability density function

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