Download presentation

Presentation is loading. Please wait.

Published byMarvin Wilkerson Modified over 2 years ago

1
Lecture (10) Mathematical Expectation

2
The expected value of a variable is the value of a descriptor when averaged over a large number theoretically infinite.

3
Mathematical Expectation (cont.) Another way to compute the variance

4
Example 1 TTTHHTHH 012 Sample SpaceNumber of Heads

5
Example 1 (cont.)

6
3210 1 0.5.25 NUMBER OF HEADS P R O B A B I L I T Y Experiment: Toss Two Coins

7
Example 1 (cont) E.G. Toss 2 coins, count heads, compute expected value: = 0 .25 + 1 .50 + 2 .25 = 1 E.G. Toss 2 coins, count heads, compute variance: variance = (0 - 1) 2 (.25) + (1 - 1) 2 (.50) + (2 - 1) 2 (.25) =.50

8
Example 2

9
Find the mean of the number of spots that appear when a die is tossed. The probability distribution is given below. Discrete Uniform Distribution Example

10
That is, when a die is tossed many times, the theoretical mean will be 3.5. That is, when a die is tossed many times, the theoretical mean will be 3.5. Discrete Uniform Distribution Example (cont.)

11
Binomial Distribution - Binomial Distribution - Example A coin is tossed four times. Find the mean, variance and standard deviation of the number of heads that will be obtained. Solution:Solution: n = 4, p = 1/2 and q = 1/2. = n p = (4)(1/2) = 2. 2 = n p q = (4)(1/2)(1/2) = 1. = = 1.

12
Poisson Distribution

13
Uniform Distribution Example

14
If the probability density function has the form f(x) = ax for a random variable X between 0 and 2. (a)Find the value of a. (b) Find the median of X (c)Find P(1.0 < X < 2.0) Solution: (a) From the area under the whole density curve is 1, then we have Example

15
Quiz

16
Exponential Distribution

17
DistributionNormal x LogN Y =logx Gamma x Exp t Mean xx yy nk1/k Variance xx yy nk 1/k 2 Skewnesszero 2/n 0.5 2 Comparison of Parameters of Dist’n

Similar presentations

OK

ฟังก์ชั่นการแจกแจงความน่าจะเป็น แบบไม่ต่อเนื่อง Discrete Probability Distributions.

ฟังก์ชั่นการแจกแจงความน่าจะเป็น แบบไม่ต่อเนื่อง Discrete Probability Distributions.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on remote operated spy robots Ppt on abo blood grouping system Perspective view ppt online Ppt on jawaharlal nehru in hindi language Ppt on breadth first search and depth first search Pdf to ppt online nitro Ppt on materialized view in oracle Ppt on world book day april Greenhouse effect for kids ppt on batteries Pdf to ppt online converter