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Lecturenotes11 - STAT 430/510 Lecture 11 STAT 430/510...

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STAT 430/510 Lecture 11 STAT 430/510 Probability Hui Nie Lecture 11 June 16th, 2009
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STAT 430/510 Lecture 11 Review Introduce continuous random variable Expected value and variance of continuous r.v.
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STAT 430/510 Lecture 11 Uniform Random Variable A continuous random variable X is said to have a uniform distribution on the interval [ A , B ] if the pdf of X is f ( x ) = 1 B - A , A x B 0 , otherwise
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STAT 430/510 Lecture 11 cdf For uniform r.v. X on [ A , B ] , the cdf is F ( x ) = 0 , m < A x - A B - A , A x B 1 , x > B
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STAT 430/510 Lecture 11 Expected Value and Variance X is uniform random variable on [ A , B ] . E [ X ] = A + B 2 E [ X 2 ] = B 2 + AB + A 2 3 Var ( X ) = ( B - A ) 2 12
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STAT 430/510 Lecture 11 Example If X is uniformly distributed over (0,10), calculate the probability that (a) X < 3 (b) X > 6 (c) 3 < X < 8 P ( X < 3 ) = R 3 0 1 10 dx = 3 10 P ( X > 6 ) = R 10 6 1 10 dx = 2 5 P ( 3 < X < 8 ) = R 8 3 1 10 dx = 1 2
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STAT 430/510 Lecture 11 Example Buses arrive at a specific stop at 15-minute interval starting at 7 A.M. That is, they arrive at 7, 7:15, 7:30, 7:45, and so on. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:30, find the probability that he waits (a) less than 5 minutes for a bus (b) more than 10 minutes for a bus
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STAT 430/510 Lecture 11
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