Question

what are the two requirements for a discrete probability distribution?

choose the correct answer below. select all that apply.

a. $\sum p(x)=1$
b. $0 < p(x) < 1$
c. $0 \leq p(x) \leq 1$
d. $\sum p(x)=0$

Explanation:

• For a discrete probability distribution, the probability of each individual outcome \(P(x)\) must satisfy \(0\leq P(x)\leq1\). This is because probability values cannot be negative (so \(P(x)\geq0\)) and cannot exceed \(1\) (so \(P(x)\leq1\)).
• Also, the sum of all probabilities for all possible discrete outcomes must equal \(1\), i.e., \(\sum P(x) = 1\). This represents the certainty that one of the discrete outcomes will occur.

Answer:

A. \(\sum P(x)=1\), C. \(0\leq P(x)\leq1\)