Here we have tablewith values for X and P(X).
As we know the sum ofall the probabilities in a probability distribution of a random variable mustbe one.
Hence the sum ofprobabilities of given table = 0.4 + 0.4 + 0.2
= 1
Hence, the given tableis the probability distributions of a random variable.
(ii)
Here we have tablewith values for X and P(X).
As we see from thetable that P(X) = -0.1 for X = 3.
It is known thatprobability of any observation must always be positive that it can’t benegative.
Hence, the given tableis not the probability distributions of a random variable.
(iii)
Here we have tablewith values for X and P(X).
As we know the sum ofall the probabilities in a probability distribution of a random variable mustbe one.
Hence the sum ofprobabilities of given table = 0.6 + 0.1 + 0.2
= 0.9 ≠ 1
Hence, the given tableis not the probability distributions of a random variable.
(iv)
Here we have tablewith values for X and P(X).
As we know the sum ofall the probabilities in a probability distribution of a random variable mustbe one.
Hence the sum ofprobabilities of given table = 0.3 + 0.2 + 0.4 + 0.1 + 0.05
= 1.05 ≠ 1
Hence, the given tableis not the probability distributions of a random variable.