The probability distribution shown below describes a population of measurements. $$\begin{array} { c | c c c }
x & 0 & 2 & 4 \
\hline p ( x ) & 1 / 3 & 1 / 3 & 1 / 3
\end{array}$$ 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)3
B)1
C)4
D)2
E)0

Question

The probability distribution shown below describes a population of measurements. $$\begin{array} { c | c c c } 
x & 0 & 2 & 4 \
\hline p ( x ) & 1 / 3 & 1 / 3 & 1 / 3
\end{array}$$ 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)3
B)1
C)4
D)2
E)0

Quizplus · Accepted Answer

The expected value of the population is calculated as $E(X) = \sum x \cdot p(x)$, which equals $0 \cdot \frac{1}{3} + 2 \cdot \frac{1}{3} + 4 \cdot \frac{1}{3} = 2$. The expected value of the sampling distribution of the sample mean is the same as the population mean, which is 2.

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