The probability distribution shown below describes a population of measurements. $$\begin{array} { c | c c c }
\mathrm { x } & 0 & 2 & 4 \
\hline \mathrm { p } ( \mathrm { x } ) & 1 / 3 & 1 / 3 & 1 / 3
\end{array}$$ Suppose that we took repeated random samples of n = 2 observations from the population described above. Find the expected value of the sampling distribution of the sample mean.
A) 0
B) 1
C) 2
D) 3
E) 4

Question

The probability distribution shown below describes a population of measurements. $$\begin{array} { c | c c c } 
\mathrm { x } & 0 & 2 & 4 \
\hline \mathrm { p } ( \mathrm { x } ) & 1 / 3 & 1 / 3 & 1 / 3
\end{array}$$ Suppose that we took repeated random samples of n = 2 observations from the population described above. Find the expected value of the sampling distribution of the sample mean.
A) 0
B) 1
C) 2
D) 3
E) 4

Quizplus · Accepted Answer

The expected value of the sampling distribution of the sample mean is equal to the expected value of the population distribution. The expected value of the population is calculated as: $E(X) = 0 \times \frac{1}{3} + 2 \times \frac{1}{3} + 4 \times \frac{1}{3} = 2$.

The Probability Distribution Shown Below Describes a Population of Measurements x024p(x)1/31/31/3\begin{array} { c | c c c } \mathrm { x } & 0 & 2 & 4 \\\hline \mathrm { p } ( \mathrm { x } ) & 1 / 3 & 1 / 3 & 1 / 3\end{array}xp(x)​01/3​21/3​41/3​​

The Probability Distribution Shown Below Describes a Population of Measurements $\begin{array} { c | c c c } \mathrm { x } & 0 & 2 & 4 \\\hline \mathrm { p } ( \mathrm { x } ) & 1 / 3 & 1 / 3 & 1 / 3\end{array}$