STAT 400 Study Guide - Final Guide: Probability Distribution, Antiderivative, Random Variable

• School: University of Maryland
• Department: Statistics and Probability
• Course: STAT 400
• Professor: Tim Pilachowski

Document Summary

Stat 400 section 4. 2 cumulative distribution functions and expected value notes by tim pilachowski. A probability density function or probability distribution function for a continuous random variable is a function f(x) such that, on an interval [a, b], A pdf f(x) has two necessary characteristics: f(x) 0 for all values of x in the interval [a, b] (since all probabilities, and therefore areas under the curve, are zero or positive) xf dx. 1= (since the sum of all probabilities = 1 = area under the curve over the entire domain) When we evaluate the integral of a probability density function for a portion of the domain from to an arbitrary value of x, Xp x x yf dy ( )xf called the cumulative distribution function. , we get another function which is an antiderivative and is. Formally, given a probability density function defined as xf. Bxa otherwise the cumulative density function will have the form.