    Question

# 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 2 1 0 −1 P (Z) 0.3 0.2 0.4 0.1 0.05

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Solution

## It is known that the sum of all the probabilities in a probability distribution is one. (i) Sum of the probabilities = 0.4 + 0.4 + 0.2 = 1 Therefore, the given table is a probability distribution of random variables. (ii) It can be seen that for X = 3, P (X) = −0.1 It is known that probability of any observation is not negative. Therefore, the given table is not a probability distribution of random variables. (iii) Sum of the probabilities = 0.6 + 0.1 + 0.2 = 0.9 ≠ 1 Therefore, the given table is not a probability distribution of random variables. (iv) Sum of the probabilities = 0.3 + 0.2 + 0.4 + 0.1 + 0.05 = 1.05 ≠ 1 Therefore, the given table is not a probability distribution of random variables.  Suggest Corrections  0      Related Videos   Axiomatic Approach
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