Answer:
Expected value = 2.7
Explanation:
The expected value of a probability distribution is given by the equation:
[tex]E(x)\text{ = }\sum ^{}_{}xP(x)[/tex][tex]E(x)=x_1P(x_1)+x_2P(x)+x_3P(x_3)+x_4P(x_4)[/tex]
From the table given:
[tex]\begin{gathered} x_1=1,P(x_1)=1/10,x_2=2,P(x_2)=3/10,x_3=3,P(x)\text{ = 4/10} \\ x_4=4,P(x_4)\text{ = 2/10} \end{gathered}[/tex]
Substitute these values into the expected value formula
[tex]\begin{gathered} E(x)\text{ = 1(}\frac{1}{10})+2(\frac{3}{10})+3(\frac{4}{10})+4(\frac{2}{10}) \\ E(x)\text{ = 1(0.1)+2(0.3)+3(0.4)+4(0.2)} \\ E(x)\text{ = 0.1 + 0.6 + 1.2 + 0.8} \\ E(x)\text{ = 2.7} \end{gathered}[/tex]
The expected value of the probability distribution = 2.7
