Can you help me with this problem?

Let $\displaystyle {X_1},{X_n},...,{X_n}$, be a random simple sample, where $\displaystyle {X_i}$ is a discrete uniform random variable on $\displaystyle \{ 1,2,3...\theta \} $.

Thus, $\displaystyle P({X_i} = x) = \frac{1}{\theta }$

Find the maximum likelihood estimate for $\displaystyle \theta $,and show it's biased.

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I managed to conclude that the maximum verosimil estimate is:

$\displaystyle {\tilde \theta _{ML}} = \max \{ {X_1},{X_2},...,{X_n}\} $

But I dont know how to show it's biased: since it's discrete random variable, i think i cant derivate.