Order of statistics problem

[xbox2kfan]

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.

Thank you.

[thanhdaica1985]

P(min Xi < q < max Xi) = 1 - P(min Xi > q)*P(q > max Xi)

P(min Xi > q) = P(X1 > q)*P(X2 > q)*P(X3 > q)
P(max Xi < q) = P(X1 < q)*P(X2 < q)*P(X3 < q)

I hope this will help you.

[NoMoreExams]

P(min Xi < q < max Xi) = 1 - P(min Xi > q)*P(q > max Xi)

P(min Xi > q) = P(X1 > q)*P(X2 > q)*P(X3 > q)
P(max Xi < q) = P(X1 < q)*P(X2 < q)*P(X3 < q)

I hope this will help you.

Deleted for now

[thanhdaica1985]

I don't understand what you mean Nomorexams.