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NOTE :- Please find the probabilities as functions of cost A service facility charges a $20 fixed...

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Statistics

NOTE :- Please find the probabilities as functions ofcost

A service facility charges a $20 fixed fee plus $25 per hour ofservice up to 6 hours, and no additional fee is charged for aservice visit exceeding 6 hours. Suppose that the service time Ï„again ranges from 0 to 10 hours, but now the probability density istwice as large during the middle 6 hours [2, 8] than during theouter 4 hours [0, 2] and [8, 10]. (Note as before that Ï„ is acontinuous random variable.) Let X represent the cost of service inthe facility.

We would like to set up the probability density function (PDF)and the cumulative distribution function (CDF), then use them toanalyze service fees.

Design Specifications

  1. Sketch the probability density as a function of time. Bequantitative, and pay attention to units. Compute the probabilitythat the service is greater than 6 hours. Then, sketch theprobability density as a function of cost. Again, be quantitativeand pay attention to units

  2. Use the probability density function to set up the cumulativeprobability, also as a function of X.

Answer & Explanation Solved by verified expert
3.9 Ratings (557 Votes)
Let bethe service time Let k bethe probability density of for and Then theprobability density for is Let bethe probability density of    See Answer
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