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Statistical Inference Question

  1. Jun 13, 2012 #1
    Hi guys,

    I am stuck with this problem... Please help!

    Define the rounding function [.] to integers as follows:

    [x] = j if x ∈ (j-0.5, j+0.5, for j = 0,+-1, +-2,...

    Suppose X has a uniform distribution on the interval (a,b). i.e., X~U(a,b) a<b.

    1. find a pair a and b such hat Var(X) > Var([X]) and such that VAR(X) < VAR([X])
    2. Suppose that a random variable X has a continuous CDF F(x). What are the distributions of F(X) and [F(X)]? and finally R = [F(X)]-F(X)?
     
  2. jcsd
  3. Jun 14, 2012 #2

    Stephen Tashi

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    Instead of what you wrote, I think the question should say:

    1. Find a pair of numbers (a,b) such that Var(X) > Var([X]) and find another pairs of numbers (a,b) such that Var(X) < Var([X]).
     
  4. Jun 15, 2012 #3

    haruspex

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    F(X) doesn't mean anything, and neither does 'the distribution of F(x)'. F(x) is the distribution of X.
    Should it read:
    What are the distributions of [X] and [X]-X?
     
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