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Following Example 4.21, let X and Y denote the arrival times of the first two calls at a telephone switch. The joint PDF of X and Y is
What is the PDF of W = Y - X?
Example 4.21
At noon on a weekday, we begin recording new call attempts at a telephone switch. Let X denote the arrival time of the first call, as measured by the number of seconds after noon. Let Y denote the arrival time of the second call. In the most common model used in the telephone industry, X and Y are continuous random variables with joint PDF.
Where λ > 0 calls/second is the average arrival rate of telephone calls. Find the marginal PDFs fX (x) and fY (y) and the conditional PDFs f X|Y (x|y) and fY |X (y|x).
Use the normal distribution below to answer the following questions. What is the mean number of hours of sleep that people get each night? What is the standard deviation of the variable "hours of sleep per night"
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