IB Maths AA HL AA 4.4 practice question

Paper 2, calculatorEasy6 marks

The parking duration $X$ in hours, of a randomly selected vehicle at a car park is modelled by the probability density function

f(x)= \begin{cases} \frac14, & 0\leq x\leq 4,\\ 0, & \text{otherwise}. \end{cases}

(a)

Find the mean parking duration $E(X)$ giving your answer in hours.

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(b)

Determine $\operatorname{Var}(X)$ giving your answer in hours squared.

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(c)

The parking charge $C$ in dollars, is given by $C=2+0.5X$ Hence find $E(C)$ and $\operatorname{Var}(C)$ giving appropriate units.

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