1 / 9

Review: INDEPENDENCE OF EVENTS

Review: INDEPENDENCE OF EVENTS. TWO EVENTS A AND B ARE SAID TO BE INDEPENDENT IF ANY OF THE FOLLOWING EQUIVALENT CONDITIONS ARE TRUE:. Chapter 12: Joint Distributions. Data classifying 356 male federal employees based on socio-economic status and smoking.

merrill-casey
Download Presentation

Review: INDEPENDENCE OF EVENTS

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Review: INDEPENDENCE OF EVENTS • TWO EVENTS A AND B ARE SAID TO BE INDEPENDENT IF ANY OF THE FOLLOWING EQUIVALENT CONDITIONS ARE TRUE:

  2. Chapter 12: Joint Distributions Data classifying 356 male federal employees based on socio-economic status and smoking

  3. Chapter 12: Joint Distributions: Intro to Modeling Variables of Interest X: Smoking and Y: Socio-economic status X = 0 mean person is current smoker X = 1 mean person is former smoker X = 2 mean person has never smoked Y = 0 mean person has high socio-economic status Y = 1 mean person has medium socio-economic status Y = 2 mean person has low socio-economic status

  4. Chapter 12: Joint Distributions Joint probability distribution for smoking and socio-economic status.

  5. Chapter 12: Joint Distributions Marginal Distribution for Smoking Marginal Distribution for socio-economic status

  6. Chapter 12: Independence and Joint Distributions Independence from a joint distribution table: Check: P(X=u , Y=v) = P(X=u)P(Y=v) Note: P(X=u , Y=v) means P(X=u and Y=v). Example: P(X=1, Y=2) = 0.079 P(X=1) = 0.396 , P(Y=2)= 0.262 P(X=1)P(Y=2) = 0.396*0.262 = 0.103752. This suffices to conclude that smoking and socio-economic status are not independent.

  7. Chapter 12: Sampling without Replacement In a drawer there are has 6 black and 8 blue socks.  Select two socks randomly. What is the probability that you get two socks that are of different color? What is the probability that the first sock is black and the second is blue?

  8. Chapter 13: Hyper Geometric Distributions Modeling “Sampling without Replacement Problems” Example: Suppose that you have a bag filled with 50 marbles, 15 of which are green. What is the probability of choosing exactly 3 green marbles if a total of 10 marbles are selected?

  9. Chapter 13: Hyper Geometric Distributions You are president of an on-campus special events organization. You need a committee of 7 to plan a special birthday party for the president of the college. Your organization consists of 18 women and 15 men. What is the probability that your committee will have 4 female?

More Related