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Question
70% of the members favour and 30% oppose a proposal in a meeting. The random variable X takes the value 0 if a member opposes the proposal and the value 1 if a member is in favour. Find E(X) and Var(X).
Solution
According to the given conditions,
P(X = 0) = `(30)/(100) = (3)/(10) "and" "P"("X" = 1) = (70)/(100) = (7)/(10)`
∴ E(X) = \[\sum\limits_{i=1}^{2} x_i\text{P}(x_i)\] = `0 xx (3)/(10) + 1 xx (7)/(10) = (7)/(10)` = 0.7
∴ E(X2) = \[\sum\limits_{i=1}^{2} x_i^2\text{P}(x_i)\] = `0^2 xx (3)/(10) + 1^2 xx (7)/(10) = (7)/(10)` = 0.7
∴ Var(X) = E(X2) – [E(X)]2 = `(7)/(10) - (7/10)^2`
= `(70 - 49)/(100)`
= `(21)/(100)`
= 0.21
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