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# Continuous Random Variables: Summary of The Uniform and Exponential Probability Distributions

Module by: Kathy Chu, Ph.D.. E-mail the author

Summary: This module provides a summary of formulas and definitions related to Continuous Random Variables.

## Formula 1: Uniform

XX = a real number between aa and bb (in some instances, XX can take on the values aa and bb). aa = smallest XX ; bb = largest XX

XX ~ U(a, b)U(a,b)

The mean is μ=a+b 2 μ a+b 2

The standard deviation is σ= (b-a)2 12 σ (b-a)2 12

Probability density function: fX = 1b-a fX=1b-a for aXb a X b

Area to the Left of x: P(X<x)=(base)(height) P(X x) (base)(height)

Area to the Right of x: P(X>x)=(base)(height) P(X x) (base)(height)

Area Between c and d: P(c<X<d)=(base)(height)=(d-c)(height) P(c X d) (base)(height) (d-c)(height).

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