1 / 16

Chris Morgan, MATH G160 csmorgan@purdue February 24, 2012 Lecture 18

Chris Morgan, MATH G160 csmorgan@purdue.edu February 24, 2012 Lecture 18. Chapter 6.1: Unifrom Distributions. Uniform Distribution. • When we worked with discrete RV’s, we came across many variables for which each outcome was equally likely such as rolling a die or flipping a coin.

gotzon
Download Presentation

Chris Morgan, MATH G160 csmorgan@purdue February 24, 2012 Lecture 18

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. Chris Morgan, MATH G160 csmorgan@purdue.edu February 24, 2012 Lecture 18 Chapter 6.1: Unifrom Distributions

  2. Uniform Distribution • When we worked with discrete RV’s, we came across many variables for which each outcome was equally likelysuch as rolling a die or flipping a coin. • In the continuous case, this type of situation is called a uniformrandom variable. • A uniform random variable is a continuous random variable for which every outcome in an interval is equally likely. NOTE: The probability that X falls in a subinterval only depends on the length (not position) of the subinterval.

  3. Uniform Distribution Examples: - X is a random variable on the closed interval from [0,1] - X is the exact time that someone will sneeze during class - often used when writing random number generators in computer science - any time we have no idea when something will occur, it is equally likely to happen at any time, so we will use uniform (similar to how we used p=0.5 previously)

  4. Uniform Distribution Notation: X ~ Uni(a, b) where: a is the lower bound, and b is the upper bound PDF: f(x) = for a ≤ x ≤ b CDF: F(x) = for a ≤ x ≤ b

  5. Uniform PDF

  6. Uniform CDF

  7. Uniform Distribution Expected Value: Variance:

  8. Uniform Example #1 Suppose you are going out for the evening with friends and they ask you to be ready to leave by 9:00pm. Your friends will arrive at a time T uniformly distributed between 9:00pm and 9:30pm. State the distribution and Parameters of T:

  9. Uniform Example #1a What is the probability that you’ll have to wait for more than 20 minutes for your friends? Remember: A CDF only tells us the probability to the left of X, so when we are looking for a value greater than X, we need to find the compliment (subtract from 1)

  10. Uniform Example #1b If at 9:20pm your friends have no yet arrived, what is the probability that you have to wait at least 5 more minutes?

  11. Uniform Example #1c What is the probability that your friends will arrive at exactly 9:25pm? Why?? - REMEMBER: with a a continuous distribution:

  12. Uniform Example #1d Find the mean and variance of wait time.

  13. Uniform Example #2a Assume that the time it takes a students to walk from one class to the next class on Purdue’s campus ranges uniformly from 0 to 15 minutes. What is the probability that a student will be late to his or her next class, if there is a 10-minute break between classes?

  14. Uniform Example #2b What is the probability that a student will make it to class in exactly five minutes?

  15. Uniform Example #2c What is the probability that it will take a student between 5 and 13 minutes to get to class, given it will take them more than four minutes to get to class?

More Related