68  Exploring tails of distributions

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a) Say I have three distributions:

• Exponential, β=1
• Normal, μ=1, σ=1
• Cauchy, µ=1, σ=1

Say I draw numbers out of each of these distributions. Rank order the distributions, lowest to highest, in terms of how likely I am do draw a number greater than 10. You do not need to calculate anything to answer this question.

b) Now draw a million numbers out of each of the three distributions. Which, if any, had numbers greater than ten? Was your intuition from part (a) correct?