Suppose that the queuing time, \(T\) (in minutes), at a customer service desk has a probability density function given by
\(f(t) = \begin {cases}
kt(16-t^2) &\ \ 0 \leq t \leq 4 \\
\\
0 &\ \ \text{elsewhere}
\end{cases}\)
for some \(K \in R\).
- Show that \(k=\dfrac{1}{64}\). (1 mark)
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- Find \(E(T)\). (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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