14111cn8.7-8

14111cn8.7-8 - • ¯ x is the expected value (mean) • σ...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
c ± Kendra Kilmer October 27, 2011 Section 8.3 - Variance and Standard Deviation Example 1: Draw the histograms for the random variables X and Y that have the following probability distribu- tions: x P ( X = x ) 1 . 1 2 . 1 3 . 6 4 . 1 5 . 1 y P ( Y = y ) 1 . 3 2 . 1 3 . 2 4 . 1 5 . 3 Definition : Suppose a random variable X has the following probability distribution: x P ( X = x ) x 1 p 1 x 2 p 2 · · · · · · x n p n and expected value E ( X ) = μ . Then the variance of the random variable X is Var( X )= p 1 ( x 1 - μ ) 2 + p 2 ( x 2 - μ ) 2 + ··· + p n ( x n - μ ) 2 . Definition : The standard deviation of a random variable X , σ , is defined by: σ = p Var ( X ) 7
Background image of page 1

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

View Full DocumentRight Arrow Icon
c ± Kendra Kilmer October 27, 2011 Finding expected value and standard deviation using the calculator: Enter the x-values into L1 and the corresponding probabilities into L2 (STAT 1:Edit) On the homescreen type 1-Var Stats L 1 , L 2 (STAT CALC 1:1-Var Stats)
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: • ¯ x is the expected value (mean) • σ x is the standard deviation • To find variance, you would need to recall that Var ( X ) = σ 2 Example 2 : Referring to Example 1, a) Find the variance and standard deviation of X . b) Find the variance and standard deviation of Y . Example 3: The percent of the voting age population who cast ballots in presidential election years from 1980 through 2000 are given below: Election Year 1980 1984 1988 1992 1996 2000 Turnout Percentage 53 53 50 55 49 51 Find the mean and standard deviation of the voter turnout. Section 8.3 Highly Suggested Homework Problems: 3, 5, 7, 9, 11, 13, 15, 22 8...
View Full Document

This note was uploaded on 03/27/2012 for the course MATH 141 taught by Professor Jillzarestky during the Fall '08 term at Texas A&M.

Page1 / 2

14111cn8.7-8 - • ¯ x is the expected value (mean) • σ...

This preview shows document pages 1 - 2. Sign up to view the full document.

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