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Math Help - Standard Uniform Distribution

  1. #1
    Super Member Deadstar's Avatar
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    Standard Uniform Distribution

    Never really did much stats so this is probably an easy question.

    What values can the standard uniform distribution take? Is it just any value between 0 and 1? Is each value chosen with equal probability?

    So for example, if I'm to asked the question...

    Calculate t_1 ~ U(0,1) where U is the uniform distribution and t is a random variable. Is that even a properly written out question? Does it just mean t will take a random value between 0 and 1?

    As I say I've not done much stats and not entirely sure what the notation stands for.
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  2. #2
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    Quote Originally Posted by Deadstar View Post
    Calculate t_1 ~ U(0,1) where U is the uniform distribution and t is a random variable. Is that even a properly written out question? Does it just mean t will take a random value between 0 and 1?
    I would say that is a good guess.
    Only your textbook can say for sure.
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  3. #3
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Deadstar View Post
    Never really did much stats so this is probably an easy question.

    What values can the standard uniform distribution take? Is it just any value between 0 and 1? Is each value chosen with equal probability?

    So for example, if I'm to asked the question...

    Calculate t_1 ~ U(0,1) where U is the uniform distribution and t is a random variable. Is that even a properly written out question? Does it just mean t will take a random value between 0 and 1?

    As I say I've not done much stats and not entirely sure what the notation stands for.

    t ~ U(0,1) means that t has a density that is 1 on (0,1) and 0 otherwise.
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  4. #4
    Super Member Deadstar's Avatar
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    Hmm I'm still not totally clear on this... Let me put down whats in the textbook. Its to do with the Kolmogorov-Smirnov distribution.

    I'm testing the hypothesis that a sample of n independent observations comes from a specified continuous distribution.
    ...Let F_0(x) be the distribution function from which, according to the hypothesis to be tested, the sample has been taken. We let x_1, x_2, \ldots , x_n denote the order statistics of the sample, and define t_j = F_0(x_j) for j = 1,2, \ldots , n.
    Then I have a formula to use.
    If the null hypothesis holds t_1, t_2, \ldots t_n are the order statistics of a random sample size n from the uniform distribution on (0,1).

    And the first thing I have written down to do (written by my prof)...
    Set n to be a fixed amount
    Calculate t_1, t_2, \ldots , t_n ~ U(0,1)

    note, F_0(x) is not given but i assume thats the empirical distribution function?

    So, given this info, how would you calculate the t's for say, n=4?

    As I say im quite new to stats and this is all the info I have. If I can calculate the t's I'm sorted for the rest of it.
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