MAT 2377 Lecture Notes - Lecture 6: Random Variable, Cumulative Distribution Function, Normal Distribution

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 2377
• Professor: Aziz Khanchi

Document Summary

Denition : a random variable x is said to be continuous if its cumu- lative distribution function fx is a continuous function. Denition : let x be a continuous random variable with the c. d. f. The probability density function of x is (cid:26) f (cid:48)(x), 0, f (x) = if f (cid:48)(x) exists, otherwise, where f (cid:48) is the derivative of f . Note : we sometimes denote the probability density function (p. d. f. ) of. Example 1 : consider a poisson process with a rate . Let x be the length of the interval required to observe a change in the poisson process. Show that the c. d. f. of x is (cid:26) 0, Note : the function f is a continuous function. Properties of f : f (x) 0 (cid:90) f (x) dx = 1. 2: [computational property] let a r, then (cid:90) P (x a) = f (x) dx.