which of the following represents a valid probability distribution?\nprobability distribution…

which of the following represents a valid probability distribution?\nprobability distribution a\n|x|p(x)|\n|----|----|\n|1|-0.14|\n|2|0.6|\n|3|0.25|\n|4|0.29|\nprobability distribution b\n|x|p(x)|\n|----|----|\n|1|0|\n|2|0.45|\n|3|0.16|\n|4|0.39|\nprobability distribution c\n|x|p(x)|\n|----|----|\n|1|0.45|\n|2|1.23|\n|3|-0.87|\n|4|0.19|

which of the following represents a valid probability distribution?\nprobability distribution a\n|x|p(x)|\n|----|----|\n|1|-0.14|\n|2|0.6|\n|3|0.25|\n|4|0.29|\nprobability distribution b\n|x|p(x)|\n|----|----|\n|1|0|\n|2|0.45|\n|3|0.16|\n|4|0.39|\nprobability distribution c\n|x|p(x)|\n|----|----|\n|1|0.45|\n|2|1.23|\n|3|-0.87|\n|4|0.19|

Answer

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

The value of (P(1)= - 0.14), which is less than 0. So, Probability Distribution A is not valid.

Step3: Check Probability Distribution B

(P(1) = 0), (P(2)=0.45), (P(3)=0.16), (P(4)=0.39). All (P(x)) values are between 0 and 1. And (0 + 0.45+0.16 + 0.39=1). So, Probability Distribution B is valid.

Step4: Check Probability Distribution C

The value of (P(2)=1.23\gt1) and (P(3)= - 0.87\lt0). So, Probability Distribution C is not valid.

Answer:

Probability Distribution B