Question

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

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.