I. Problem
In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is se-
lected at random and we take X = 0 if he opposed, Download latex code from hereand X = 1 if he is in favour. Find E(X) and Var (X).
II. Solution
A member opposes the proposal : X=0;
A member favours the proposal : X=1;
P(X=0) = 70 % = 0.7 P(X=1) = 30 % =0.3
n
X
E(X) = xipi
i=1
(1)
= 1 × 0.7 + 0 × 0.3 = 0.7
(2)
=⇒ E(X) = 0.7
(3)
n
2 X 2
E(X ) = (xi) pi
i=1
(4)
= 12 × 0.7 + 02 × 0.3 = 0.7
(5)
Var(X) = E(X2) − [E(X)]2
(6)
= 0.7 − 0.72 = 0.21
(7)
=⇒ Var(X) = 0.21
(8)
Similar result is also obtained with random samples generated using the python code.
Figure 1: Result obtained from python code
