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lecture6 - LECTURE VI STAT 515 February 2, 2010 University...

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Unformatted text preview: LECTURE VI STAT 515 February 2, 2010 University of South Carolina Lecture 6 – p.1 Mean and standard deviation • Let X ∼ Uniform(c,d), then the probability density function is given by f ( x ) = 1 d- c for c ≤ x ≤ d. • It can be computed that μ := E [ X ] = c + d 2 σ = d- c √ 12 . • P ( a < X < b ) = ( b- a ) / ( d- c ) for c ≤ a < b ≤ d . Remember P ( a < X < b ) = the area cut by x=a,x=b, and the density. Lecture 6 – p.2 Exercise 3 • An unprincipled used-car dealer sells a car to an unsuspecting buyer, even though the dealer knows that the car will have a major breakdown within the next 6 months. The dealer provides a warranty of 45 days on all cars sold. Let X represent the length of time until the breakdown occurs. Assume that X is a uniform random variable with values between 0 and 6 months. (a). Calculate the mean and standard deviation of X . (b). Calculate the probability that the breakdown occurs while the car is still under warranty....
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This note was uploaded on 06/06/2011 for the course STAT 515 taught by Professor Zhao during the Spring '10 term at South Carolina.

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lecture6 - LECTURE VI STAT 515 February 2, 2010 University...

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