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. ∑(p_i) = 1

Given distribution is :

Clearly,

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

= 0.6 + 0.4 + 0.2

= 1.2 ≠ 1

∴ The given distribution is not a probability distribution.