\begin{tabular}{c|cccc}
[tex]$x$[/tex] & 1 & 4 & 7 & 10 \\
\hline
[tex]$P(x)$[/tex] & 0.2 & 0.2 & 0.2 & 0.4
\end{tabular}

The expected value of this probability distribution is:

A. 10.0
B. 5.5
C. 6.4



Answer :

To find the expected value of the given discrete probability distribution, we follow these steps:

1. List the values and their corresponding probabilities:
[tex]\[ \begin{array}{c|cccc} x & 1 & 4 & 7 & 10 \\ \hline P(x) & 0.2 & 0.2 & 0.2 & 0.4 \\ \end{array} \][/tex]

2. Multiply each value [tex]\( x \)[/tex] by its corresponding probability [tex]\( P(x) \)[/tex]:
- For [tex]\( x = 1 \)[/tex], [tex]\( P(x) = 0.2 \)[/tex]:
[tex]\[ 1 \times 0.2 = 0.2 \][/tex]
- For [tex]\( x = 4 \)[/tex], [tex]\( P(x) = 0.2 \)[/tex]:
[tex]\[ 4 \times 0.2 = 0.8 \][/tex]
- For [tex]\( x = 7 \)[/tex], [tex]\( P(x) = 0.2 \)[/tex]:
[tex]\[ 7 \times 0.2 = 1.4 \][/tex]
- For [tex]\( x = 10 \)[/tex], [tex]\( P(x) = 0.4 \)[/tex]:
[tex]\[ 10 \times 0.4 = 4.0 \][/tex]

3. Sum up all these products to get the expected value:
[tex]\[ 0.2 + 0.8 + 1.4 + 4.0 = 6.4 \][/tex]

Therefore, the expected value of this probability distribution is:
[tex]\[ \boxed{6.4} \][/tex]