Question

In a meeting, 70% of the members favour a certain proposal, 30% being opposite. 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 variance (X).

Answer 1

Answer:

E(X) = 0.7

var(X) = 0.21

I hope this helps.

Step-by-step explanation:

For the random variable X, we have

P(X=0) = P(member is opposed) = 0.3

P(X=1) = P(member is in favour) = 0.7

So

E(X)  =  0×P(X=0) + 1×P(X=1)  =  0×0.3 + 1×0.7  =  0.7

E(X²)  =  0²×P(X=0) + 1²×P(X=1)  =  0×0.3 + 1×0.7  =  0.7

var(X) = E(X²) - [E(X)]²  =  0.7 - 0.7² = 0.7 - 0.49  = 0.21