The random variable $$\(X\)$$ has the discrete uniform distribution $$\[ \mathrm{P}(X=x)=\frac{1}{\alpha} \quad \text { for } x=1,2, \ldots, \alpha \]$$ The mean of a random sample of size $$\(n\)$$, taken from this distribution, is denoted by $$\(\bar{X}\)$$ Use the sample mean to estimate the value of $$\(\alpha\)$$ (2)

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