1 / 13

Understanding Discrete Probability Distributions and Random Variables

This chapter delves into discrete probability distributions and the nature of random variables. A random variable is defined as a variable where the outcome is a numerical result of a random phenomenon, such as counting heads in coin tosses. Discrete random variables take on countable values, while continuous random variables can assume any value in an interval. We explore probability distributions, their representations, and calculate probabilities for scenarios, including gender probabilities in families and outcomes from rolling dice.

muncel
Download Presentation

Understanding Discrete Probability Distributions and Random Variables

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. CHAPTER 5:Discrete Probability Distributions 5.1 Probability Distributions

  2. Random Variables A random variable is a variable whose value is a numerical outcome of a random phenomenon. • let X = number of heads. • if we get HHTH, X = 3 • if we get TTTH, X = 1 • What is the sample space for X?

  3. Random Variables • they are variables because they keep changing • they are random because we don’t know the next value the variable will assume. • we DO know the overall pattern of the values assumed by a random variable over many repetitions.

  4. Random Variables • A discrete random variable has a countable number of possible values. • usually counts

  5. ounces Random Variables • A continuous random variable can take any value in an interval of the real number line. • usually measurements

  6. DISCRETE orCONTINUOUS? • weight of a book • number of chapters in a book • number of defects in a square yard of fabric • number of homeruns in a season • weight of a boat-load of fish

  7. DISCRETE Random Variables • We will use capital letters to represent discrete random variables • usually X or Y • corresponding lower case letters will represent values of the random variable. • P(X = x) is the probability that the random variable X equals the value x.

  8. DISCRETE Random Variables • the probability distribution of Xlists the values and their probabilities. • Every piis between 0 and 1. • the sum of the p’s is 1.

  9. DISCRETE Random Variables • Find the probability distribution for a gender for a family with three single births. • Express P(at least two boys) in terms of X. • find it.

  10. DISCRETE Random Variables • Create a Probability Distribution for rolling a six sided die.

  11. DISCRETE Random Variables • 25% of women cannot distinguish between the colors red and green. • Find the probability distribution for 3 randomly chosen women. • So, what is the probability that exactly two women will be colorblind? • What is the probability that at least one will not be colorblind?

  12. DISCRETE Random Variables Create a Probability Distribution for the following: The probabilities of a return on an investment of 1000, 2000, 3000 are ½, ¼, and ¼ respectively.

  13. DISCRETE Random Variables Create a Probability Distribution for the following: A die is weighted so that the probabilities of getting 1, 2, 3, 4, 5, and 6 are ½, 1/6, 1/12, 1/12, 1/12, and 1/12 respectively.

More Related