Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $\{X_i\}$ be $n$ iid dunif(0, u) (discrete uniform) random variables with u>n. How do I compute the probability that $\{X_{i+1}\}$ > $\{X_i\}$ for all i?

share|improve this question
    
The title and body contain different questions. The question in the title would correspond to the question in the body with $\gt$ replaced by $\ge$. Please clarify which of these is your actual question. –  joriki Aug 30 '12 at 1:17
    
youre right. i meant strictly greater than –  Wuschelbeutel Kartoffelhuhn Aug 30 '12 at 1:20

1 Answer 1

up vote 4 down vote accepted

Because of a comment by the OP, I will interpret the uniform as having possible values $1,2,3,\dots,u$, a total of $u$ values. It is easy to alter the expression below to deal with another interpretation.

Record the result of the $n$ experiments as a sequence $(x_1,x_2,\dots,x_n)$. Then all $u^n$ sequences are equally likely.

The number of ways to choose a strictly increasing sequence $(x_1,x_2,\dots,x_n)$ is $\binom{u}{n}$. for there are $\binom{u}{n}$ ways to select the set of values, and for every such set, only one sequence made up of elements of the set qualifies as increasing.

For the probability, divide by $u^n$. The result is $$\frac{\binom{u}{n}}{u^n}.$$

share|improve this answer
    
In the books I've read, the second argument of dunif() is always part of the sample space. Thanks a lot for the answer. –  Wuschelbeutel Kartoffelhuhn Aug 30 '12 at 1:18
    
The answer I got from simulations corresponds to the one I get from your formula. Thanks again. –  Wuschelbeutel Kartoffelhuhn Aug 30 '12 at 1:25

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.