Three actuaries are independently hired to appraise the value of acompany. The true value of the company is q million dollars, and each actuary’sestimate is uniformly distributed between q – 2 million dollars and q + 3 milliondollars. Find the probability that the actual value of q lies between the lowest andthe highest estimate.

That is, let X1 , X2 , X3 be i.i.d. Uniform( q – 2, q + 3 ).Find the probability
P(min Xi < q < max Xi ).

Hint: It is easier to find the probability of the complement.

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