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4.2.1 Expectation and Mean

Let c be a constant, for example let c = 5.

∑ E[X ] = pi(xi) = μx


∑ ∑ E [cX ] = pi(cxi) = c pi(xi) = cμx

∑ ∑ E [5X ] = pi(5(xi)) = 5 pi(xi) = 5μx


∑ ∑ ∑ ∑ E [X + c] = pi(xi + c) = pi(xi) + pi(c) = μx + c pi = μx + c

∑ ∑ ∑ ∑ E[X + 5] = pi(xi + 5) = pi(xi) + pi(5) = μx + 5 pi = μx + 5


If you have a summation of something over i that doesn’t change for any of the i, for example a constant c, or 5 it can be moved outside of the summation, as was done above.

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