Methods2023 Exam 1 · Q8Tech-free6 marks

Queuing time probability density function

Suppose that the queuing time, $T$ (in minutes), at a customer service desk has a probability density function given by

$f(t) = \begin{cases} kt(16 - t^2) & 0 \le t \le 4 \\ 0 & \text{elsewhere} \end{cases}$

Show that $k = \frac{1}{64}$ .

1 mark

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Find $\operatorname{E}(T)$ .

2 marks

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What is the probability that a person has to queue for more than two minutes, given that they have already queued for one minute?

3 marks

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