Loading…

Flash Player 9 (or above) is needed to view presentations.
We have detected that you do not have it on your computer. To install it, go here.

Like this presentation? Why not share!

Like this? Share it with your network

Share

Cumulative distribution

on

  • 680 views

 

Statistics

Views

Total Views
680
Views on SlideShare
680
Embed Views
0

Actions

Likes
0
Downloads
5
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Cumulative distribution Presentation Transcript

  • 1. 1
    Cumulative distribution function &Expectation
    Shashwat Shriparv
    dwivedishashwat@gmail.com
    InfinitySoft
  • 2. 2
    In modeling real-world phenomena there are few situations where the actions of the entities within the system under study can be completely predicted in advance.
    The world the model builder sees is probabilistic rather than deterministic
  • 3. 3
    An appropriate model can be developed by sampling the phenomenon of interest.
    Then, through educated guesses the model builder would select a known distribution form, make an estimate of the parameter of this distribution, and then test to see how good a fit has been obtained.
  • 4. 4
    Review of terminology & concepts
    Discrete random variables.
    Continuous random variables.
    Cumulative distribution function
    Expectation
  • 5. 5
    Cumulative Distribution Function
  • 6. 6
    The cumulative distribution function (cdf), denoted by F(x), measures the probability that the random variable X assumes a value less than or equal to x,
    that is,
    F(x)=P(X<=x).
  • 7. 7
    Properties of the cdf
    F is a non-decreasing function, If a<b, then F(a)<=F(b).
    Lim x->-∞ F(x)=0.
    Lim x->∞ F(x)=1.
  • 8. 8
    Expectation
  • 9. 9
    An important concept in probability theory is that of the expectation of a random variable.
    if x is a random variable, the expected value of X, is denoted by E(X).
  • 10. 10
    The expected value E(X) of a random variable X is also referred to as the mean, or the first moment of X.
    The variance of a random variable, X, is denoted by V(X) of var(X), is defined as V(X)=E[(X-E[X])²]
    And also
    V(X)=E(X²)-[E(X)]²
  • 11. 11
    The mean E(X) is a measure of the central tendency of a random variable.
    The variance of X measures the expected value of the squared difference between the random variable and its mean.
    Thus the variance, V(X), is a measure of the spread or variation of the possible values of X around the mean E(X).
  • 12. 12
    Thank yoU
    Shashwat Shriparv
    dwivedishashwat@gmail.com
    InfinitySoft