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CONTINUOUS RANDOM VARIABLES AND PDFS

A random variable X is called continuous if there is a non-negative function f_x , called the probability density function of X, or pdf such that $$P (X \in B) = \int_B f_X(x) dx$$, for every subset B of the real line. In particular, the value of X falls within an interval is

$$P (a \leq X \leq b) = \int_a^b f_X(x) dx$$

PDF fx follows following properties $$f_X(x) \geq 0 \space for \space all \space x \space and$$

$$\int_{-\infty}^{\infty} f_X(x) dx = 1$$