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).

Given: X = 0 if members oppose, and X = 1 if members are in favour.

P(X = 0)

P(X = 1)

Hence, the required probability distribution is,

X | 0 | 1 |

P(X) | 0.3 | 0.7 |

Therefore E(X) is:

= 0 × 0.3 + 1 × 0.7

⇒ E(X) = 0.7

And E(X^{2}) is:

= (0)^{2} × 0.3 + (1)^{2} × 0.7

⇒ E(X^{2}) = 0.7

Then Variance, Var(X) = E(X^{2}) – (E(X))^{2}

= 0.7 – (0.7)^{2}

= 0.7 – 0.49 = 0.21

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