Continuous Random Variable

Definition (Continuous Random variable).

SaY a Continuous Random Variable if there exist a function such that

Remark.

Example

but it if the set is uncountable then this does not hold true

Remark.

Let then there are (uncountably) infinitely many values of other than

Definition (Cummulative distribution function).

Definition (Exponential density function).

Theorem.

from first fundamental theorem of Calculus wiki
if is continuous at

If X is continuous RV with distribution function and density function f(X) , find the density function of (pg no. 188 1d)