In a meeting, $70 %$ of the members favor 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 favor. Find the mean and variance of $X$ .

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Solution

$n = 1, p (X = 0) = q = 0.3$
$p (X = 1) = p = 0.7$
So, Mean $= n p = 1 (0.7) = 0.7$
Variance $= n p q = 1 \times 0.7 \times 0.3 = 0.21$

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In a meeting, 70% of the members favor 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 favor. Find the mean and variance of X.

n=1,p(X=0)=q=0.3p(X=1)=p=0.7So, Mean=np=1(0.7)=0.7Variance=npq=1×0.7×0.3=0.21

In a meeting, $70 %$ of the members favor 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 favor. Find the mean and variance of $X$ .

$n = 1, p (X = 0) = q = 0.3$
$p (X = 1) = p = 0.7$
So, Mean $= n p = 1 (0.7) = 0.7$
Variance $= n p q = 1 \times 0.7 \times 0.3 = 0.21$