Skip to content Skip to navigation

Connexions

You are here: Home » Content » Continuous Random Variables: Summary of The Uniform and Exponential Probability Distributions

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

      A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

      What is in a lens?

      Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

      Who can create a lens?

      Any individual Connexions member, a community, or a respected organization.

    • External bookmarks
  • E-mail the authors

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

This content is ...

In these lenses

  • Bio 502 at CSUDH

    This module is included inLens: Bio 502
    By: Terrence McGlynnAs a part of collection:"Collaborative Statistics"

    Comments:

    "This is the course textbook for Biology 502 at CSU Dominguez Hills"

    Click the "Bio 502 at CSUDH" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

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

Module by: Dr. Barbara Illowsky, Susan Dean

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 a<X<b a X b or a≤X≤b a X b

Area to the Left, Right and Inbetween: P(X<x)=(a base)(height) P(X x) (a base)(height)

P(X>x)=(a base)(height) P(X x) (a base)(height)

P(c<X<d)=(a base)(height)=(d-c)(height) P(c X d) (a base)(height) (d-c)(height).

formula 2: Exponential

XX ~ Exp (m)Exp(m)

XX = a real number, 0 or larger. mm = the parameter that controls the rate of decay or decline

The mean and standard deviation are the same.

μ=σ= 1mμ=σ=1m and m= 1μ= 1σm=1μ=1σ

The probability density function: f(X) =m⋅ e-m⋅Xf(X)=m⋅e-m⋅X

Area to the Left: P(X<x)=1- e-m⋅x P(X x) 1- e-m⋅x

Area to the Right: P(X>x)= e-m⋅x P(X x) e-m⋅x

Area Inbetween: P ( c < X < d ) = P ( X < d ) - P ( X < c ) = ( 1 - e − m⋅d ) - ( 1 - e − m⋅c ) = e − m⋅c - e − m⋅d P ( c X d ) = P ( X d ) - P ( X c ) =(1- e − m⋅d )-(1- e − m⋅c )= e − m⋅c - e − m⋅d

Percentile, k: k = LN(1-AreaToTheLeft) -m k= LN(1-AreaToTheLeft) -m

Comments, questions, feedback, criticisms?

Send feedback