Consider the Probability Distribution Shown Here 62 Properties of Sampling Distributions: Unbiasedness and Minimum Variance 1

Essay

Consider the probability distribution shown here. $$\begin{array}{l}\begin{array} { l | r r r } \hline x & 1 & 3 & 5 \\\hline p ( x ) & \frac { 1 } { 3 } & \frac { 1 } { 3 } & \frac { 1 } { 3 } \\\hline\end{array}\\\\\text { Let } \bar { x } \text { be the sample mean for random samples of } n = 2 \text { measurements from this distribution. Find } E ( x ) \text { and } E ( \bar { x } ) \text {. }\end{array}$$ 6.2 Properties of Sampling Distributions: Unbiasedness and Minimum Variance 1 Understand Unbiasedness