In a meeting, $70 %$ of the members favour a certain proposal, $30 %$ being opposite. A member is selceted at random and let X=0, if he opposed and X=1, if he is in favour. Find E(X) and V(X)

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Solution

It is given that P(X=0)= $30 % = \frac{30}{100} = \frac{3}{10}$

$P (X = 1) = 70 % = \frac{70}{100} = \frac{70}{100}$
therefore , the probability distrinution is as follows

$\begin{matrix} x & 0 & 1 P (x) & \frac{3}{10} & \frac{7}{10} \end{matrix}$

$∴ M e a n o f X = E (x) = \sum X p (X) = 0 \times \frac{3}{10} + 1 \times \frac{7}{10} = \frac{7}{10}$
Variance of $X = \sum x^{2} P (X) - (M e a n)^{2} = 0^{2} \times \frac{3}{10} + 1^{2} \times \frac{7}{10} - {(\frac{7}{10})}^{2} = \frac{7}{10} - \frac{49}{100} = \frac{21}{100}$

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In a meeting, 70% of the members favour a certain proposal, 30% being opposite. A member is selceted at random and let X=0, if he opposed and X=1, if he is in favour. Find E(X) and V(X)

It is given that P(X=0)= 30%=30100=310 P(X=1)=70%=70100=70100 therefore , the probability distrinution is as follows x01P(x)310710 ∴ Mean of X =E(x)=∑Xp(X)=0×310+1×710=710 Variance of X=∑x2P(X)−(Mean)2=02×310+12×710−(710)2=710−49100=21100

In a meeting, $70 %$ of the members favour a certain proposal, $30 %$ being opposite. A member is selceted at random and let X=0, if he opposed and X=1, if he is in favour. Find E(X) and V(X)