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Markov's Inequality

  1. Nov 17, 2007 #1
    Markov's Inequality !!!!

    Let X be uniformly distributed over (1,4)

    (a) Use Markov's inequlaity to estimate P(x>=a) a is between 1 to 4 and compare this result to the exact answer.

    (b) Find the value of a in (1,4) that minimizes the difference between the bound and the exact probability computed in (a).

    For this question i used
    EX= (a+b)/2 since its uniformly distributed so i got EX=5/2 which means that the probability of X being greater than or equal to a is less than 5/2a. For the exact value I got the dist function of a uniform RV as being (x-a)/(b-a) so the F(x) should be (a-1)/4. The exact value is 1-(a-1)/4 so i got the exact value as being (4-a)/3.(b) I had (4-a)/3 <= 5/2a and then got them to one side took the derivative and set it equal to 0 and got 2.738

    Was this right? Thanks!
  2. jcsd
  3. Nov 18, 2007 #2


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    Science Advisor
    Homework Helper

    For (a), may need to formally show actual value < upper bound.

    For (b), I'd check the second derivative, to be safe.
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