Download
1 / 24

Lecture12 - PowerPoint PPT Presentation


  • 304 Views
  • Uploaded on

5-1 Two Discrete Random Variables. Example 5-1.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Lecture12' - Roberta


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
5 1 two discrete random variables l.jpg
5-1 Two Discrete Random Variables

Example 5-1

Calls are made to check the airline schedule at your departure city. You monitor the number of bars of signal strength on your cell phone and the number of times you have to state the name of your departure city before the voice system recognize the name. Define:

X = number of bars of signal strength on your cell phone

Y = denote the number of times you need to state your departure city


5 1 two discrete random variables4 l.jpg
5-1 Two Discrete Random Variables

Figure 5-1Joint probability distribution of X and Y in Example 5-1.


5 1 two discrete random variables5 l.jpg
5-1 Two Discrete Random Variables

5-1.1 Joint Probability Distributions


5 1 two discrete random variables6 l.jpg
5-1 Two Discrete Random Variables

5-1.2 Marginal Probability Distributions

  • The individual probability distribution of a random variable is referred to as its marginal probability distribution.

  • In general, the marginal probability distribution of X can be determined from the joint probability distribution of X and other random variables. For example, to determine P(X =x), we sum P(X =x, Y =y) over all points in the range of (X, Y ) for which X =x. Subscripts on the probability mass functions distinguish between the random variables.



5 1 two discrete random variables8 l.jpg
5-1 Two Discrete Random Variables

Figure 5-2Marginal probability distributions of X and Y from Figure 5-1.


5 1 two discrete random variables9 l.jpg
5-1 Two Discrete Random Variables

Definition: Marginal Probability Mass Functions


5 1 two discrete random variables10 l.jpg
5-1 Two Discrete Random Variables

5-1.3 Conditional Probability Distributions


5 1 two discrete random variables11 l.jpg
5-1 Two Discrete Random Variables

5-1.3 Conditional Probability Distributions


Slide12 l.jpg

5-1 Two Discrete Random Variables

Definition: Conditional Mean and Variance


Slide13 l.jpg

Example 5-4

Figure 5-3Conditional probability distributions of Y given X,fY|x(y) in Example 5-4.


5 1 two discrete random variables14 l.jpg
5-1 Two Discrete Random Variables

5-1.4 Independence

Example 5-6


Slide15 l.jpg

Example 5-8

Figure 5-4(a)Joint and marginal probability distributions of X and Y in Example 5-8. (b) Conditional probability distribution of Y given X = x in Example 5-8.



5 1 two discrete random variables17 l.jpg
5-1 Two Discrete Random Variables

5-1.5 Multiple Discrete Random Variables

Definition: Joint Probability Mass Function


5 1 two discrete random variables18 l.jpg
5-1 Two Discrete Random Variables

5-1.5 Multiple Discrete Random Variables

Definition: Marginal Probability Mass Function


5 1 two discrete random variables19 l.jpg
5-1 Two Discrete Random Variables

Example 5-8

Figure 5-5Joint probability distribution of X1, X2, and X3.


5 1 two discrete random variables20 l.jpg
5-1 Two Discrete Random Variables

5-1.5 Multiple Discrete Random Variables

Mean and Variance from Joint Probability


5 1 two discrete random variables21 l.jpg
5-1 Two Discrete Random Variables

5-1.5 Multiple Discrete Random Variables

Distribution of a Subset of Random Variables


5 1 two discrete random variables22 l.jpg
5-1 Two Discrete Random Variables

5-1.5 Multiple Discrete Random Variables

Conditional Probability Distributions


5 1 two discrete random variables23 l.jpg
5-1 Two Discrete Random Variables

5-1.6 Multinomial Probability Distribution


5 1 two discrete random variables24 l.jpg
5-1 Two Discrete Random Variables

5-1.6 Multinomial Probability Distribution