{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Week 4 Mon Sept 20

# Week 4 Mon Sept 20 - WEEK 4 Monday Sept 20 Today Cover...

This preview shows pages 1–4. Sign up to view the full content.

1 WEEK 4, Monday , Sept 20 Today: Cover Sections 3-1 through 3-3 . Discuss discrete and continuous random variables and their distributions as probability models. Outcomes are on the real number line, often the events of interest are intervals. Discrete Probability mass function . Properties are p ( x ) where p ( x ) ≥ 0 (3-1) and 1 ) ( x all x p . (3-2) Cumulative distribution function . x i i p x X P x F ) ( ) ( ) ( (3-3) Expectation . ) ( ) ( all x x xp X E (3-4) is called the mean of X or simply the expected value of X . For any function h and Y = h ( X ), Y is a random variable with expectation x all x p x h X h E Y E ) ( ) ( )) ( ( ) ( . (3-5) Variance and Standard Deviation . )] ( [ ) ( ] ) [( ) ( 2 2 2 2 2 2 x p x X E X E X V (3-7) and (3-8) ) ( ) ( X V X SD (3-9)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Please note . The units of measure for E ( X ) and SD ( X ) are the same as the units of measure for X . If X is measured in feet , then E ( X ) and SD ( X ) are in units of feet . If X is in units of (\$1,000), then E ( X ) and SD ( X ) are in units of (\$1,000). Example 1. Total on the roll of a pair of fair dice . x 2 3 4 5 6 7 8 9 10 11 12 p ( x ) 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36 Probability Mass Function p and Cumulative Distribution Function F x p (x) F ( x ) 2 1/36 1/36 3 2/36 3/36 4 3/36 6/36 5 4/36 10/36 6 5/36 15/36 7 6/36 21/36 8 5/36 26/36 9 4/36 30/36 10 3/36 33/36 11 2/36 35/36 12 1/36 36/36 Prob Dist of X = Total on Two Dice 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 2 3 4 5 6 7 8 9 10 11 12 x P(x)
3 Prob Dist of X = Total on Two Dice 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 2 3 4 5 6 7 8 9 10 11 12 x P(x) Way to Calculate Mean, Variance, and Standard Deviation of a Discrete Random Variable 7 ) ( ) ( x xp X E 8333 . 5 36 / 210 7 ) 36 / 1974 ( ) ( ] ) [( ) ( 2 2 2 2 2 X E X

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern