Q48

Let $X$ be a random variable which takes values in the set $\{1,2,3,4,5,6,7,8\}$. Further, $\operatorname{Pr}(X=1)=\operatorname{Pr}(X=2)=\operatorname{Pr}(X=5)=\operatorname{Pr}(X=7)=\frac{1}{6}$ and $\operatorname{Pr}(X=3)=\operatorname{Pr}(X=4)=\operatorname{Pr}(X=6)=\operatorname{Pr}(X=8)=\frac{1}{12}$. The expected value of $X$, denoted by $E[X]$, is equal to $\_\_\_\_$. (rounded off to two decimal places)