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Unformatted text preview: EXERCISES IN STATISTICS Exercise M01 1. The probability density function governing the minutes of time t spent waiting outside a telephone box is given by f ( t ) = ae at . (a) Determine the probability of having to wait for more than t minutes. (b) Show that the probability of having to wait more than 2 t minutes, given that you have waited for t , is the same as the unconditional probability of having to wait more than t minutes. What are the implications of this result? Answer. (a)The probability of having to wait more than t minutes is given by (1) Z t f ( t ) dt = 1 Z t f ( t ) dt = 1 e at t = 1 + e at 1 = e at . (b) The probability of having to wait 2 t minutes given that you have already waited for t ie. given that you will have to wait more than t is (2) P ( x > 2 t | x > t ) = P ( x > 2 t ) P ( x > t ) = e 2 at e at = e at ....
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- Spring '12