which of the following represents a valid probability distribution? probability distrbution a x p(x) 1 -0.14…

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

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

Answer

Explanation:

Step1: Check probability rules

For a valid probability distribution, (0\leq P(x)\leq1) and (\sum P(x) = 1).

Step2: Analyze Distribution A

(P(1)=- 0.14<0), violates (0\leq P(x)\leq1).

Step3: Analyze Distribution B

(P(1) = 0), (P(2)=0.45), (P(3)=0.16), (P(4)=0.39). (\sum P(x)=0 + 0.45+0.16 + 0.39=1) and (0\leq P(x)\leq1) for all (x).

Step4: Analyze Distribution C

(P(2)=1.23>1) and (P(3)=-0.87<0), violates (0\leq P(x)\leq1).

Answer:

Probability Distribution B.