[20pts] A service facility charges a $20 fixed fee plus $25 per hour of service up to 6 hours, and no additional fee is charged for a service visit exceeding 6 hours. Suppose (for now) that the service time τ is equally likely to be any time in [0, 10] hours. (Note that τ is a continuous random variable.) Let X represent the cost of service in the facility. We would like to set up the probability density function (PDF) and the cumulative distribution function (CDF), then use them to analyze service fees.

Step-by-step explanation:

The function of a continuous random variable, whose integral over an interval provides the likelihood that the value of the variable is just inside the same interval while The cumulative distribution function (FX) provides the possibility that the random variable X is not up to or equal to a particular amount x. the formula for calculating it is: Summing the values for every one of the outcomes less than or equal to x will give the solution.

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step-by-step explanation:

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