Banner Ad 1

Collapse

Announcement

Collapse
No announcement yet.

Order of statistics problem

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • Order of statistics problem

    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.

  • #2
    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.

    Comment


    • #3
      Originally posted by thanhdaica1985 View Post
      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
      Last edited by NoMoreExams; September 12 2011, 02:13 PM.

      Comment


      • #4
        I don't understand what you mean Nomorexams.

        Comment

        Working...
        X