Question

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

Answer 1

It is given that P(X = 0) = 30% =$\frac{30}{100}=0.3$

P(X=1)=70%=$\frac{70}{100}=0.7$

Therefore, the probability distribution is as follows.

X	0	1
P(X)	0.3	0.7

xt pt xtpt xtpt2
0 $\frac{30}{100}$
1$\frac{ 70}{100}\frac{70}{100}\frac{ 70}{100}$
$∑ptxt=70/100 ∑ptxt2=\frac{70}{100}$
$E(X)=Mean=∑ptxt=\frac{70}{100}=0.7$
$Vrience(X)=∑ptxt2-(∑ptxt)2=\frac{70}{100}-(\frac{70}{100})2=\frac{7}{10}-\frac{49}{100}=\frac{21}{100}=0.21$

=0.21