Notes 125-137 - STAT 155 Section 4.4 The Exponential and Gamma Distributions There are many practical situations in which the variable of interest to an

# Notes 125-137 - STAT 155 Section 4.4 The Exponential and...

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STAT 155 Section 4.4: The Exponential and Gamma Distributions______________________________ There are many practical situations in which the variable of interest to an investigator might have a skewed distribution. One family of distributions that has this property is the gamma family. We first consider a special case, the exponential distribution, and then generalize later in the section. . The exponential distribution is often known as the distribution of the amount of time until some specific event occurs. For example, the amount of time from now until an earthquake occurs. ______________________________________________ E(X) = 1/ and Var(X) = 1/ 2 ______________________________________________ Example: Suppose the response time X at a certain on-line computer terminal (the elapsed time between the end of a user’s inquiry and the beginning of the system’s response to that inquiry) has an exponential distribution with expected response time equal to 5 sec. What is the probability that the response time is at most 10 sec? .