Question

Find the standard deviation of the discrete random variable X with the following probability distribution, X={3, 2, 1, 0} and P(X) = {.125, .375, .375, .125}

Answer 1

$\mu=3*0.125+2*0.375+1*0.375+0*0.125=1.5.$

$\sigma=\sqrt{3^2*0.125+2^2*0.375+1^2*0.375+0^2*0.125-1.5^2}=\sqrt{0.75}\approx0.866.$