State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

Answer

N/a

Explanation

We know that the sum of all probabilities of a probality distribution is 1.
(i) Sum of probability `=0.4+0.4+0.2=1`
Therefore given table is the probability distribution of a random variable.
(ii) It can be seend that for `X=3,P(X)=-0.1`
The probability given table is not the probability distribution of a random variable.
(iii) Here all probabilities are positive but their sum is less than 1. Therefore given distribution is not a probability distribution.
`(0.6+0.1+0.2=0.9lt1)`
(iv) Here all probabilities are positive but their sum is more than 1.
`(0.3+0.2+0.4+0.1+0.05=1.05gt1)` ltrbgt Therefore given distribution is ot a probability distribution.