Question

determine whether the following is a probability distribution. if not, identify the requirement that is not satisfied.

x	p(x)
0	0.280
1	0.288
2	-0.045
3	0.061
4	0.288
5	0.128

probability distribution.
not a probability distribution. one of the p(x)s is negative.
not a probability distribution. the sum of the p(x)s is not 1.

Explanation:

Step1: Recall probability - distribution requirements

A probability - distribution has two requirements: 1. \(0\leq P(x)\leq1\) for all \(x\). 2. \(\sum_{x}P(x)=1\).

Step2: Check non - negativity

We see that \(P(2)= - 0.045\lt0\). Since one of the \(P(x)\) values is negative, it does not satisfy the first requirement.

Answer:

Not a probability distribution. One of the \(P(x)\)'s is negative.