Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 12 Oct 2017 My Price 3.00

distribution function

Suppose that Y is a random variable that takes on only integer values 1, 2, . . . . Let F(y) denote the distribution function of this random variable. As discussed in Section 4.2, this distribution function is a step function, and the magnitude of the step at each integer value is the probability that Y takes on that value. Let U be a continuous random variable that is uniformly distributed on the interval (0,1). Define a variable X such that X = k if and only if F(k−1) U ≤ F(k), k = 1, 2, . . . . Recall that F(0) = 0 because Y takes on only positive integer values. Show that P(X = i ) = F(i )− F(i −1) = P(Y = i ), i = 1, 2, . . . . That is, X has the same distribution as Y .

 

 

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Maurice Tutor
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Status NEW Posted 12 Oct 2017 11:10 AM My Price 3.00

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