Which of the following distributions of probabilities of a random variable X are the probability distributions?
(i)

X : 3 2 1 0 −1

P (X) : 0.3 0.2 0.4 0.1 0.05

(ii)

X : 0 1 2

P (X) : 0.6 0.4 0.2

(iii)

X : 0 1 2 3 4

P (X) : 0.1 0.5 0.2 0.1 0.1

(iv)

X : 0 1 2 3

P (X) : 0.3 0.2 0.4 0.1

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Solution

(i) P (X = 3) + P (X = 2) + P (X = 1) + P (X = 0) + P (X = $-$ 1)
= 0.3 + 0.2 + 0.4 + 0.1 + 0.05
=1.05 > 1
It is not the probability distribution of random variable X.

(ii) P (X = 0) + P (X = 1) + P (X = 2)
= 0.6 + 0.4 + 0.2
= 1.2 > 1
It is not the probability distribution of random variable X.

(iii) P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)
= 0.1 + 0.5 + 0.2 + 0.1 + 0.1
= 1
It is the probability distribution of random variable X.

(iv) P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
= 0.3 + 0.2 + 0.4 + 0.1
= 1
It is the probability distribution of random variable X.

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