Let y be a random variable with p (y) given in the accompanying table. find e (y), e (1/y), e (y 2 - 1), and v (y). y 1 2 3 4 p (y).4.3.2.1

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4 November, 20:28

Let y be a random variable with p (y) given in the accompanying table. find e (y), e (1/y), e (y 2 - 1), and v (y). y 1 2 3 4 p (y).4.3.2.1

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Everett Wu · Answer 1

E[Y] = 0.4·1 + 0.3·2 + 0.2·3 + 0.1·4 = 2 E[1/Y] = 0.4·1/1 + 0.3·1/2 + 0.2·1/3 + 0.1·1/4 = 0.4 + 0.15 + 0.0666 + 0.025?0.64 V[Y] = E[Y2]-E[Y]2 = (0.4) ·12 + (0.3) ·22 + (0.2) ·32 + (0.1) ·42-22 = 0.4+1.2+1.8+1.6-4 = 5-4 = 1