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Unformatted text preview: ISyE 2027 Probability with Applications Polly B. He Fall10, Week 5 Reading: Section 5.2-5.3, 7.1 The Uniform Distribution Definition: A continuous random variable has a uniform distribution on the interval [ α,β ] if its probability density function f is given by f ( x ) = 1 β- α if α ≤ x ≤ β elsewhere We denote this distribution by U ( α,β ). If X ∼ U ( α,β ), find the distribution function of X . Example 5.2.1 Buses arrive at a specific stop at 15-minute intervals starting at 7 A.M. (i.e., 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 less than 5 minutes for a bus. 1 Where do we use the uniform distribution? The uniform distribution is useful when you have no information about a variable of interest except its upper and lower bounds....
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- Fall '08
- Probability theory, Exponential distribution, probability density function, Polly B. He Fall10