- 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 \(\bar { X }\)
- Show that \(2 \bar { X }\) is a biased estimator of \(\alpha\)
A random sample of 6 observations of \(X\) is taken and the results are given below.
$$\begin{array} { l l l l l l }
8 & 7 & 3 & 7 & 2 & 9
\end{array}$$
- Use the sample mean to estimate the value of \(\alpha\)