which of the following is a valid probability distribution? probability distribution a x p(x) 1 0.42 2 0.38…

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

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

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

(\sum_{x = 1}^{4}P(x)=0.42 + 0.38+0.13 + 0.07=1), and (0\leq0.42\leq1), (0\leq0.38\leq1), (0\leq0.13\leq1), (0\leq0.07\leq1).

Step3: Check Probability Distribution B

(\sum_{x = 1}^{4}P(x)=0.27+0.28 + 0.26+0.27 = 1.08\neq1), so it is not a valid probability - distribution.

Step4: Check Probability Distribution C (incomplete in the image, but assume the sum condition is violated if not all values are shown)

Since the sum of probabilities for a valid distribution must be 1, and without all values for Distribution C, if we assume the sum is not 1, it is not valid.

Answer:

Probability Distribution A is a valid probability distribution.