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JonoPUH
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Homework Statement
Let Yn be uniform on {1, 2, . . . , n} (i.e. taking each value with probability 1/n). Draw the distribution function of Yn/n. Show that the sequence Yn/n converges in distribution as n → ∞. What is the limit?
Homework Equations
So Yn has c.d.f Yn(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 Yn by n, and so plot |x|/n2?
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 Yn/n clearly tends to 0 as n → 0 since we have 1/n.
Thanks
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