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GO Classes CS/DA Test Series 2025 | Probability and Statistics | Topic Wise Test 3 | Question: 7

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By the reasoning above, we can express $E[X]$ in a recursive fashion and solve for it.

$$
\begin{aligned}
E[X] & =\frac{1}{6} \cdot 1+\frac{5}{6}(E[X]+1) \\
& =\frac{1}{6}+\frac{5}{6}+\frac{5}{6} E[X] \\
\frac{1}{6} E[X] & =1 \\
E[X] & =6
\end{aligned}
$$

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