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$$E[S] = \frac{1}{10} \sum\_{i=1}^{10} i \cdot P(Y = 1 | X = i) = \frac{1}{10} ( 1 \cdot 0 + 2 \cdot 1 + 3 \cdot 0 + 4 \cdot 1 + 5 \cdot 0 + 6 \cdot 1 + 7 \cdot 0 + 8 \cdot 1 + 9 \cdot 0 + 10 \cdot 1) = 3$$
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$$E[S] = \frac{1}{10} \sum\_{i=1}^{10} i \cdot P(Y = 1 | X = i) = \frac{1}{10} ( 1 \cdot 0 + 2 \cdot 1 + 3 \cdot 0 + 4 \cdot 1 + 5 \cdot 0 + 6 \cdot 1 + 7 \cdot 0 + 8 \cdot 1 + 9 \cdot 0 + 10 \cdot 1) = 3$$
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