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$F_i=n {m-i \choose n-1}$

where $m \ge n, 1 \le i \le m-n+1$

For instance, if $m=10, n=5$, I can draw a line graph. enter image description here

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In your example, $i$ should only go up to $6$? – GEdgar Sep 17 '11 at 19:34
@GEdgar Yes, it should terminate at 6 in this case. – Fan Zhang Sep 17 '11 at 19:37
In what sense is this a "distribution"? It just looks like a sequence to me. – Daniel McLaury Sep 17 '11 at 19:40
@user3296 The $\sum F_i$ should be normalized to 1. – Fan Zhang Sep 17 '11 at 19:42
up vote 1 down vote accepted

Except for the factor $n$, it is (reversed) a certain column in Pascal's triangle. Your example is $5{j\choose 4}$ for $j$ from $0$ to $9$. In your picture $j$ numbers it from right to left, while numbers it $i$ from left to right.

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