Question

at least one of the individual probabilities (individual items in the second column) is less than 0 or greater than 1. the probabilities in the second column do not add up to 1. the random variable is not numerical. question: look at the table below. why is this table not a probability distribution? x p(x) red.60 blue.20 green.10 yellow.10 a. the probabilities in the second column do not add up to 1. b. the random variable is not numerical. c. at least one of the individual probabilities (individual items in the second column) is less than 0 or greater than 1. question: look at the table below. why is this table not a probability distribution? x p(x) 0.65 1 3.20 2 1.12 3.45 a. at least one of the individual probabilities (individual items in the second column) is less than 0 or greater than 1. b. the random variable is not numerical.

Explanation:

Step1: Check probability rules

Probability distribution rules: \(0\leq P(X)\leq1\) for each value of \(X\), and \(\sum P(X) = 1\).

Step2: Analyze first table

In the first table, \(P(X = 1)=3.20>1\) and \(P(X = 2)=1.12>1\), \(P(X = 3)=0.45\) (but the individual probabilities (for \(x = 1\) and \(x = 2\)) violate \(0\leq P(X)\leq1\) rule.

Step3: Analyze second table

In the second table, \(\sum P(X)=0.60 + 0.20+0.10 + 0.10=1\), but \(X\) (Yellow, Green, Blue, Red) is a non - numerical random variable. A probability distribution requires the random variable \(X\) to be numerical.

Answer:

For the first question (left - hand table): A. At least one of the individual probabilities (individual items in the second column) is less than 0 or greater than 1.
For the second question (right - hand table): B. The random variable is not numerical.