Question: a random variable x has a probability density function?
Answer: Definition of the Probability Density Function. The probability that a random variable X X X takes a value in the (open or closed) interval [ a , b ] [a,b] [a,b] is given by the integral of a function called the probability density function f X ( x ) f_X(x) fX​(x): P ( a ≤ X ≤ b ) = ∫ a b f X ( x ) d x .