Question

determine whether this table represents a probability distribution.

x	p(x)
0	0.2
1	0.2
2	0.2
3	0.4

no, it is not a probability distribution
yes, it is a probability distribution

Explanation:

Step1: Check probability range

All $P(x)$ values ($0.2, 0.2, 0.2, 0.4$) are between $0$ and $1$.

Step2: Sum of probabilities

Calculate $\sum_{i}P(x_i)=0.2 + 0.2+0.2 + 0.4$.
$0.2 + 0.2+0.2 + 0.4=1$.
Since all probabilities are between $0$ and $1$ and their sum is $1$, it meets the criteria for a probability - distribution.

Answer:

Yes, it is a probability distribution