STA 301 - Ch 04 - pp 55-63

STA 301 - Ch 04 - pp 55-63 - Chapter 4 Mathematical...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 4: Mathematical Expectation 55 CHAPTER 4 — MATHEMATICAL EXPECTATION In Chapter 1 we examined numerical summaries for distributions of data sets. In Chapter 4, we extend these ideas to random variables. MEAN OF A DISCRETE RANDOM VARIABLE Example : Suppose a driver’s education instructor recorded the number of attempts each of his 50 students required to pass the road test. The data are summarized below: Number of Attempts(x) Frequency Relative Frequency 1 30 30 / 50 = .60 2 10 10 / 50 = .20 3 5 5 / 50 = .10 4 3 3 / 50 = .06 5 2 2 / 50 = .04 Total 50 50 / 50 = 1.00 Two methods to calculate the mean of the data set: • Using frequencies • Using relative frequencies Now, suppose a student is randomly selected from this class. Let X be the random variable representing the number of attempts it took the student to pass the road test. Then the probability function is: ( 29 = = = = = = 5 04 . 4 06 . 3 10 . 2 20 . 1 60 . x if x if x if x if x if x f Calculating the mean of a discrete random variable is similar to calculating the mean of a data set using relative frequencies. Chapter 4: Mathematical Expectation 56 The mean or expected value of a discrete random variable X is given by: ( 29 ( 29 ∑ = = x x x xf X E μ Calculate the expected value of X in the above example: Example : (p. 109, Ex. 4.2) In a gambling game a man is paid $5 if he gets all heads or all tails when three coins are tossed, and he will pay out $3 if either one or two heads show. and he will pay out $3 if either one or two heads show....
View Full Document

Page1 / 9

STA 301 - Ch 04 - pp 55-63 - Chapter 4 Mathematical...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online