Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability (resit) / 9 / b / v

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- Solution v

Solution

The standard normal distribution has mean zero and variance one, so

E [Z^{2}] = var (Z) + (E [Z])^{2} = 1

. Part (iv) therefore gives

E [X] = \frac{π}{2} .

Using the second moment from part (iii),

var (X) = E [X^{2}] - (E [X])^{2} = 2 - \frac{π}{2} = \frac{4 - π}{2} .

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