STA 301 - Ch 04 - pp 64-69

STA 301 - Ch 04 - pp 64-69 - Chapter 4: Mathematical...

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Chapter 4: Mathematical Expectation 64 Example : Recall our earlier example about selling magazine subscriptions. The probability function for the number of magazine subscriptions sold, X , is: ( 29 ( 29 x x f - = 4 10 1 , for { } 3 , 2 , 1 , 0 x We have already determined that the expected number of subscriptions sold, , X μ is 1. Determine the standard deviation for the number of subscriptions sold. We have two equivalent formulas for the variance of a data random variable: the “definitional” and “computational” formulas. Definitional formula: ( 29 { } 2 2 σ - = X E Computational formula: ( 29 2 2 2 - = X E Proof (discrete case):
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65 Example : (p. 122, #4.39) Recall our earlier example about the number of hours a family runs its vacuum cleaner. The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a continuous random variable X that has density function ( 29 < - < < = elsewhere x x x x x f , 0 2 1 , 2 1 0 , We have already determined that the expected number of hours run is 100. Determine the standard deviation number of hours run in a year.
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This note was uploaded on 04/17/2008 for the course STA 301 taught by Professor Noe during the Spring '08 term at Miami University.

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STA 301 - Ch 04 - pp 64-69 - Chapter 4: Mathematical...

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