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

Answer :

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. ∑(p_{i}) = 1

Given distribution is :

Clearly,

Sum of probabilities = 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

∴ The given distribution is a probability distribution.

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