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

The key point to solve the problem:


A given distribution of probabilities of a random variable X is said to be probability distribution if the sum of probabilities associated with each random variable is equal to 1


i.e. ∑(pi) = 1


Given distribution is :



Clearly,


Sum of probabilities = P(X = -1) + P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)


= 0.3 + 0.2 + 0.4 + 0.1 + 0.05


= 1.05 ≠ 1


∴ The given distribution is not a probability distribution.


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