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The waiting time until service at a hospital emergency department is modeled with the pdf $f (x) = \frac{1}{9} x \quad 0<x<3$ hours and $f (x) = \frac{2}{3}-\frac{1}{9} x \quad 3<x<6.$ Determine the following: (a) Probability the wait is less than 4 hours (b) Probability the wait is more than 5 hours (c) Probability the wait is less than or equal to 30 minutes (d) Waiting time that is exceeded by only 10% of patients (e) Mean waiting time

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