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Continuous and Discrete Probability Distributions

This guide explores the differences between discrete and continuous random variables, highlighting their characteristics. Discrete variables have specific boundaries (like the number of pages in a book) while continuous variables lack distinct boundaries (like the thickness of a book). It includes examples for classification, such as the number of steps taken and volume of water in the ocean. Additionally, the document explains how to find probabilities for continuous variables using distribution, illustrated by an example involving fruit fly life expectancy.

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Continuous and Discrete Probability Distributions

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  1. Continuous and Discrete Probability Distributions Sections 7.1 and 8.1

  2. Continuous vs. discrete A discrete random variable has definite boundaries between the different outcomes

  3. Continuous vs. discrete A continuous random variable, has no distinct boundary between the outcomes

  4. Classify the following as discrete or continuous random variables 1 – The number of steps you take to get home 2 – The number of pages in a book 3 – The thickness of a book 4 – The number of litres of water in the ocean 5 – The volume of water in the ocean 6 – Your height 7 – How many inches tall you are

  5. Probability of a Continuous Random Variable To find the probability of a continuous random variable, we can look at the probability distribution Eg) The life expectancy of a fruit fly is uniformly distributed from 10 to 30 hours

  6. The life expectancy of a fruit fly is uniformly distributed from 10 to 30 hours • What is • What is • What is • What is e) What is p(X = 25)?

  7. Estimating Continuous Data from Discrete Information • Measure your height in inches and make a frequency diagram for the class Frequency Height (inches)

  8. Try these: Continuous vs. Discrete Data • Pg. 371, read example 1 • Pg. 371 #1 Recognizing Continuous Data Sets • Pg. 419 #1, 2, 3a, b, 6

  9. Summarize in your own words: • What is the difference between a discrete and continuous random variable? • How do you calculate the probability of a continuous random variable?

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