Explain why the Expected Value of 100 rolls of a fair die is 3.5
If a fair die is rolled one time then,
E(x) = 1 * (1/6) + 2 * (1/6) + 3 * (1/6) + 4 * (1/6) + 5 * (1/6) +
6 * (1/6)
E(x) = 1/6 * (1 + 2 + 3 + 4 + 5 + 6)
E(x) = (1 /6) * 21
E(x) = 3.5
Similarlly if a fair die is rolled 100 times then
E(x) = (1/100)*{(1/6 * (1 + 2 + 3 + 4 + 5 + 6) + 1/6 * (1 + 2 + 3 +
4 + 5 + 6) + .........+ 1/6 * (1 + 2 + 3 + 4 + 5 + 6)}
E(x) = (1/100)* {100/6 * (1 + 2 + 3 + 4 + 5 + 6)}
E(x) = 1/6 * (1 + 2 + 3 + 4 + 5 + 6)
E(x) = (1 /6) * 21
E(x) = 3.5
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