Each row in the table below is a Proposed grade distribution

Each row in the table below is a Proposed grade distribution for a class. Identify each as a valid or invalid probability distribution, and explain your reasoning.

Solution

A valid probability distirbution must have probabilities sum up to 1, and all probabilities must be positive.

Thus,

a) INVALID, since 0.3 + 0.3 + 0.3 + 0.2 + 0.1 = 1.2.

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b) VALID, as 0+0+1+0+0 = 1.

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c) INVALID, as 0.3+0.3+0.3+0+0 = 0.9.

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d) INVALID, as some probabilities are negative.

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e) VALID, as 0.2+0.4+0.2+0.1+0.1 = 1.

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f) INVALID, as some probabilities are negative.