Let X be a random variable with EX 4 and EX2 21 Let hX 2X

Let X be a random variable with E(X) = 4 and E(X^2) = 21. Let h(X) = 2X -6. What are the values of E(h(X)) and Var(h(X))?

(a) 36 and 20 (b) 2 and 20 (**) (c) 65 and 42 (d) 2 and 10

Solution

h(X) = 2X -6

E{h(x)} = 2E(x)-6

= 8-6

= 2

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Var(h(x)) = Var(2x-6)

= 4Var(x)-0

= 20

Note:

Var(x) = E(x²) - Mean² = 21-16 =5

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OPtion (b) is right.