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 :
X: |
0 |
1 |
2 |
3 |
P(X): |
0.3 |
0.2 |
0.4 |
0.1 |
Clearly,
Sum of probabilities = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= 0.3 + 0.2 + 0.4 + 0.1
= 1
∴ The given distribution is a probability distribution.