An expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment and is calculated by multiplying each possible outcome by the respective probability and then summing all of those values, that is,
[tex]E=\Sigma_ix_i\times P(x_i)[/tex]
By substituting the given values into the expected value formula, we get
[tex]E=-1.25\times0.6+(-0.25)\times0.2+0\times0.1+0.50\times0.1[/tex]
which gives
[tex]E=-0.75-0.05+0+0.05[/tex]
Therefore, the expected value is:
[tex]E=-0.75[/tex]
