The expected value of a distribution(when the distribution is discrete) is given by:
[tex]E\lbrack X\rbrack=\sum ^k_{n\mathop=1}x_np_n(x_n)[/tex]
Since we have only two values, k=2.
[tex]E\lbrack X\rbrack=x_1p_1+x_2p_2[/tex]
From the table, we get the following information:
[tex]\begin{gathered} x_1=10 \\ x_2=30 \\ p_1=0.1 \\ p_2=0.3 \end{gathered}[/tex]
Then, our expected value is:
[tex]E\lbrack X\rbrack=10\times0.1+30\times0.3[/tex]
Then, solving this calculation we have:
[tex]E\lbrack X\rbrack=10[/tex]
