To obtain the value of x2, the following steps are necessary:
Step 1: Recall the formula for E(X) from probability theory, as follows:
From probability theory:
[tex]E(X)=\sum ^n_{i=1}X\cdot P(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2)+\cdots+X_n\cdot P(X_n)[/tex]
Step 2: Apply the formula to the problem at hand to obtain the value pf x2, as follows:
[tex]\begin{gathered} \text{Given that:} \\ E(X)=108 \\ X_1=80,P(X_1)=0.3 \\ X_2=?,P(X_2)=0.7 \end{gathered}[/tex]
We now apply the formula, as below:
[tex]\begin{gathered} E(X)=\sum ^2_{i=1}X\cdot P(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2) \\ \text{Thus:} \\ E(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2) \\ \Rightarrow108=(80)\times(0.3)+X_2\times(0.7) \\ \Rightarrow108=24+X_2\times(0.7) \\ \Rightarrow108-24=X_2\times(0.7) \\ \Rightarrow84=X_2\times(0.7) \\ \Rightarrow X_2\times(0.7)=84 \\ \Rightarrow X_2=\frac{84}{(0.7)}=120 \\ \Rightarrow X_2=120 \end{gathered}[/tex]
Therefore, the value of x2 is 120
