- #1

JonoPUH

- 11

- 0

## Homework Statement

Let Y

_{n}be uniform on {1, 2, . . . , n} (i.e. taking each value with probability 1/n). Draw the distribution function of Y

_{n}/n. Show that the sequence Y

_{n}/n converges in distribution as n → ∞. What is the limit?

## Homework Equations

So Y

_{n}has c.d.f Y

_{n}(x) = |x|/n where |x| is the nearest integer less than x.

## The Attempt at a Solution

Is it ok for me to just divide the c.d.f of Y

_{n}by n, and so plot |x|/n

^{2}?

This seems far too easy for 2nd year of university (I really do not trust myself with probability) and also it only gives a total for x > n of 1/n. Is this allowed?

If so, then Y

_{n}/n clearly tends to 0 as n → 0 since we have 1/n.

Thanks

Last edited: