Question

which table is a probability distribution table? x 1 2 3 4 p 0.2 0.35 0.15 0.25 x 1 2 3 4 p -0.2 -0.1 0.4 0.3 x 1 2 3 4 p 0.4 1.05 0.02 0.35 x 1 2 3 4 p 0.4 0.15 0.25 0.2

Explanation:

Step1: Check probability rules

For a probability distribution table, two rules must be satisfied: \(0\leq P(X)\leq1\) for each \(X\), and \(\sum P(X) = 1\).

Step2: Analyze first table

Sum of probabilities: \(0.2 + 0.35+0.15 + 0.25=0.95
eq1\)

Step3: Analyze second table

Negative probabilities (\(- 0.2\) and \(-0.1\)) violate \(0\leq P(X)\leq1\)

Step4: Analyze third table

\(P(X = 2)=1.05>1\) violates \(0\leq P(X)\leq1\)

Step5: Analyze fourth table

Sum of probabilities: \(0.4+0.15 + 0.25+0.2=1\), and \(0\leq0.4\leq1\), \(0\leq0.15\leq1\), \(0\leq0.25\leq1\), \(0\leq0.2\leq1\)

Answer:

The fourth table (with \(X = 1,2,3,4\) and \(P=0.4,0.15,0.25,0.2\) respectively) is a probability distribution table.