Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 18 / c / iii / Solution

For $t\ge 0$, evaluate the survival function directly:At $t=\mu +2\sigma =(2+2\sqrt{2})/\lambda$, this becomesThe parameter $\lambda$ cancels because the threshold scales with the distribution. Also $\mu -2\sigma <0$ lies outside the support, so in this particular case the two-sided event $|X-\mu |>2\sigma$ has the same probability as the stated upper-tail event.