8.1 Continuous Probability Distribution

Discrete Vs. Continuous Last chapter we dealt mostly with discrete data (number of things happening that usually involves counting). In this chapter we are going to look more at continuous variables.

Continuous Random Variable Many Natural Phenomenon are Continuous (fractions/decimals) and require a continuous distribution to be modeled. – Ex: Measurements » Lengths, Heights, Time, Lifespans, etc

Continuous Random Variable A continuous random variable X measures a continuous quantity.

Continuous Unlike a discrete random variable which we studied in Chapter 7, a Continuous Random Variable, is one that assume an Uncountable number of values We cannot list the possible values because they are an infinite number of them. Because there is an infinite number of values, the probability of each individual value is virtually 0.

Probability with Continuous With a Discrete random Variable like tossing a due, it is meaningful to talk about P(X=5) In a Continuous setting, the probability the random variable is exactly 5 is infinitesimally small, so P(X=5)=0

Types Of Curves Bell CurveBimodal 2 Modes Positive SkewNegative SkewUniform Heights of People Shoe sizes in School Populations Many students with size 7 and size 9 Number of children in Canadian families Many small families, few large families Time needed to finish 2 hour exam Few people finish early, many will use a lot of the time The probability of rolling dice. Each of the outcomes is equally likely

Uniform Distribution The download time of a video from youtube is found to range evently between 22 and 39 seconds. – What is the probability that the download will take less than 30 seconds? – What is the probability that the download will take between 30 and 35 seconds?

Assignment Pg 419 Communicate your understanding #’s 1,2ac Apply Section #’s 1-4