If given the expected value $E(X) = 3.08$ of the followingprobability Table: $$ \begin{array}{l|c|c|c|c|c|c|c|c} S & a & b & c & \hphantom{0}d\hphantom{0} & \hphantom{0}e\hphantom{0} & \hphantom{0}f\hphantom{0} & g & h \\ \hline \text{PMF} & 0.04 & 0.05 & 0.01 & \color{red}? & \color{red}? & 0.2 & 0.05 & 0.03 \\ \hline X & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \end{array}$$ is it possible to determine $P(d)$ and $P(e)$?
I have attempted to solve this problem by summing all probabilities times their respective $X$, setting it equal to $3.08$, and solving for the missing probabilities. But since there are two of them missing, I can't solve for them.
The only way I can thing of is to assume that their probabilities are equal but the problem doesn't specify that they are.
How do you solve for $P(d)$ and $P(e)$, if possible?
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