Question 381445
1) {{{mu = 0*0.25 + 1*0.40 + 2*0.20 + 3*0.15 = 0.40 + 0.40 + 0.45 = 1.25}}}
{{{sigma = sqrt((0-1.25)^2*0.25 + (1-1.25)^2*0.40 + (2-1.25)^2*0.20 + (3-1.25)^2*0.15) = sqrt(0.390625 + 0.025+0.1125+0.459375) = sqrt(0.9875) = 0.99373}}}.

2) E(-3X-2) = -3E(X) - 2 = -3*1.25-2 = -5.75.
{{{Var(-3X - 2) = 9Var(X)}}}. This means {{{sqrt(Var(-3X - 2)) = 3sqrt(Var(X)) = 3sigma}}}. Hence standard deviation of Y = -3X-2 is 3*0.99373 = 2.98119.