Question

determine whether this table represents a probability distribution.

x	p(x)
0	0.25
1	0.1
2	0.15
3	0.5

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

Explanation:

Step1: Check non - negativity

All $P(x)$ values $0.25, 0.1, 0.15, 0.5$ are non - negative.

Step2: Check sum of probabilities

Calculate $\sum_{x}P(x)=0.25 + 0.1+0.15 + 0.5$.
$0.25+0.1 + 0.15+0.5=1$.

Answer:

Yes, it is a probability distribution