Question

which of the following is a valid probability distribution? probability distribution a x p(x) 1 0.42 2 0.38 3 0.13 4 0.07 probability distribution b x p(x) 1 0.27 2 0.28 3 0.26 4 0.27 probability distribution c x p(x) 1 0.16 2 0.39 3 0.18

Explanation:

Step1: Recall probability - distribution rules

A valid probability - distribution must satisfy two conditions: 1. $0\leq P(x)\leq1$ for all $x$, 2. $\sum_{x}P(x) = 1$.

Step2: Check Probability Distribution A

Calculate the sum of probabilities: $0.42 + 0.38+0.13 + 0.07=1$. Also, each $P(x)$ is between $0$ and $1$.

Step3: Check Probability Distribution B

Calculate the sum of probabilities: $0.27+0.28 + 0.26+0.27 = 1.08
eq1$. So, it is not a valid probability - distribution.

Step4: Check Probability Distribution C

The sum of probabilities for the given values: $0.16+0.39 + 0.18=0.73
eq1$. So, it is not a valid probability - distribution.

Answer:

Probability Distribution A