Question: b) Let X be a random variable with a

b) Let X be a random variable with a <= X <= b and E(X) = mu. Show that: (i) a <= mu <= b; (ii) 0<= Var(X) <= (mu - a)(b - mu) <= (1/4)*(b - a)^2; (iii) 0 <= SD(X) <= (b - a)/2.

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