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State which of the following are not the probability distributions of a random variable. Give reasons for your answer. (i) x 0 1 2 P(X) 0.4 0.4 0.2 (ii) x 0 1 2 3 4 P(X) 0.1 0.5 0.2 -0.1 0.3 (iii) y -1 0 1 P(y) 0.6 0.1 0.2 (iv) z 3 3 1 0 -1 P(z) 0.3 0.2 0.4 0.1 0.05 Select the correct answer from above options

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(i) x 0 1 2 T P(x) 4 4 2 1 (ii) x 0 1 2 3 T P(x) .1 .5 .2 -.1 1 It is not P.d as P(X) < 0 when x = 3 (iii) Y -1 0 1 T P(Y) .6 .1 .2 .9 It is not P.d as ΣP(X) = .9 ≠1 (iv) z 3 3 1 0 T P(z) .3 .2 .4 .1 1.05 It is not a P.d as ΣP(X) = 1.05 > 1

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