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 $\displaystyle t_1$ ~ $\displaystyle U(0,1)$ 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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Originally Posted by Deadstar

Calculate $\displaystyle t_1$ ~ $\displaystyle U(0,1)$ 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?

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I would say that is a good guess.
Only your textbook can say for sure.

Quote:

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Originally Posted by Deadstar

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 $\displaystyle t_1$ ~ $\displaystyle U(0,1)$ 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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$\displaystyle t$ ~ $\displaystyle U(0,1)$ means that t has a density that is 1 on (0,1) and 0 otherwise.

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 $\displaystyle F_0(x)$ be the distribution function from which, according to the hypothesis to be tested, the sample has been taken. We let $\displaystyle x_1, x_2, \ldots , x_n$ denote the order statistics of the sample, and define $\displaystyle t_j = F_0(x_j)$ for $\displaystyle j = 1,2, \ldots , n$.
Then I have a formula to use.
If the null hypothesis holds $\displaystyle t_1, t_2, \ldots t_n$ 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 $\displaystyle t_1, t_2, \ldots , t_n $ ~ U(0,1)

note, $\displaystyle F_0(x)$ 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.