QuestionPractice Exercises 1) Which of the following are valid probability distributions? Explain a) \begin{tabular}{|c|c|} \hline & \\ \hline 0 & 0.5 \\ \hline 1 & 0.25 \\ \hline 2 & 0.25 \\ \hline \end{tabular} b) \begin{tabular}{|c|c|} \hline & \\ \hline 0.5 & 0.2 \\ \hline 0.2 & 0.3 \\ \hline 0.3 & 0.25 \\ \hline \end{tabular} c) \begin{tabular}{|c|c|} \hline & \\ \hline 0 & 0.3 \\ \hline 1 & 0.25 \\ \hline 2 & 0.25 \\ \hline 3 & 0.2 \\ \hline \end{tabular}
Studdy Solution
STEP 1
1. A valid probability distribution must satisfy two conditions: - All probabilities must be non-negative. - The sum of all probabilities must equal 1.
STEP 2
1. Verify non-negativity of probabilities for each distribution.
2. Verify that the sum of probabilities equals 1 for each distribution.
STEP 3
For distribution (a), list the probabilities:
Verify non-negativity:
All probabilities are non-negative.
STEP 4
For distribution (a), calculate the sum of probabilities:
The sum is 1, so distribution (a) is valid.
STEP 5
For distribution (b), list the probabilities:
Verify non-negativity:
All probabilities are non-negative.
STEP 6
For distribution (b), calculate the sum of probabilities:
The sum is 1, so distribution (b) is valid.
STEP 7
For distribution (c), list the probabilities:
Verify non-negativity:
All probabilities are non-negative.
STEP 8
For distribution (c), calculate the sum of probabilities:
The sum is 1, so distribution (c) is valid.
All distributions (a), (b), and (c) are valid probability distributions.
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