which of the following is a valid probability distribution?\nprobability distribution a\n|x|p(x)|\n|1|0.42|\n…

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

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

Answer

Explanation:

Step1: Recall probability - distribution rules

A valid probability distribution must satisfy two conditions: 1. (0\leq P(x)\leq1) for all (x), and 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, (0\leq0.42\leq1), (0\leq0.38\leq1), (0\leq0.13\leq1), (0\leq0.07\leq1).

Step3: Check Probability Distribution B

Calculate the sum of probabilities: (0.27+0.28 + 0.26+0.27 = 1.08\neq1). So, it is not a valid probability - distribution.

Step4: Check Probability Distribution C

The sum of probabilities is (0.16 + 0.39+0.18=0.73\neq1). So, it is not a valid probability - distribution.

Answer:

Probability Distribution A