Which of the following probability distributions is/are NOT valid complete probability distribution(s)?A X Probability0 0.12 0.23 0.34 0.4B X Probability0 0.150.5 0.151 0.201.5 0.252 0.25C X Probability0 −0.051 0.202 0.253 0.354 0.40Only Table A is an invalid distribution.Only Table B is an invalid distribution.Only Table C is an invalid distribution.
Question
Which of the following probability distributions is/are NOT valid complete probability distribution(s)?A X Probability0 0.12 0.23 0.34 0.4B X Probability0 0.150.5 0.151 0.201.5 0.252 0.25C X Probability0 −0.051 0.202 0.253 0.354 0.40Only Table A is an invalid distribution.Only Table B is an invalid distribution.Only Table C is an invalid distribution.
Solution
A valid probability distribution is one where the probabilities of all outcomes sum up to 1 and each individual probability is between 0 and 1, inclusive.
Let's check each table:
Table A: The probabilities sum up to 1 (0.1 + 0.2 + 0.3 + 0.4 = 1), and each individual probability is between 0 and 1. So, Table A is a valid probability distribution.
Table B: The probabilities do not sum up to 1 (0.15 + 0.15 + 0.20 + 0.25 + 0.25 = 1), and each individual probability is between 0 and 1. So, Table B is not a valid probability distribution.
Table C: The probabilities sum up to 1 (-0.05 + 0.2 + 0.25 + 0.35 + 0.4 = 1.15), but one of the probabilities is negative, which is not valid. So, Table C is not a valid probability distribution.
Therefore, the correct answer is "Only Table B and Table C are invalid distributions."
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