lec4.8 - 95 Lecture 10: CHAPTER 4: COMMONLY USED...

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95 Lecture 10: CHAPTER 4: COMMONLY USED DISTRIBUTIONS The Exponential Distribution – Cont’d (Section 4.7, page 261) Recall: Last class we introduced the Exponential distribution: Definition We proved proportions last class to be: Now let’s take a look at the mean and variance of the Exponential Distribution: A variable X is said to have an exponential distribution with parameter 0 if the density function for X is 0 0 0 ) ( x x e x f x If X is a random variable whose distribution is exponential with parameter , we write ) ( ~ Exp X .
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96 Mean and Variance of the Exponential Distribution: Show the mean of the exponential distribution is 1 : If ) ( ~ Exp X , then 1 x 2 2 1 x Note: The mean and variance can be computed by using integration by parts.
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Example: The response time (sec) at a certain on-line computer has an exponential distribution with 2 . 0 . a) What proportion of response times are at least 10 seconds?
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lec4.8 - 95 Lecture 10: CHAPTER 4: COMMONLY USED...

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