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Probability

Question

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In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).

Solution

X takes the values 0, 1 with probability

30 over 100 space and space 70 over 100.

straight mu space equals space sum straight x space straight p subscript straight i space equals space 7 over 10 space equals space 0.7 straight sigma squared space equals space sum space straight x space squared space straight p subscript straight i space minus space straight mu squared space equals space 7 over 10 minus 49 over 100 space equals space fraction numerator 70 minus 49 over denominator 100 end fraction space equals space 21 over 100 space equals space 0.21

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