Question

Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1, respectively, that 0, 1, 2, or 3 power failures will strike a certain subdivision in any given year. Find the mean and variance of the random variable X representing the number of power failures striking this subdivision.

Answer 1

$\mu=\Sigma_{i=1}^4x_ip(x_i)=0*0.4+1*0.3+2*0.2+3*0.1=1.$

$\sigma^2=\Sigma_{i=1}^4x_i^2p(x_i)-\mu^2=0^2*0.4+1^2*0.3+2^2*0.2+3^2*0.1-1^2=1.$