Determine whether or not the following distribution is a probability distribution. If the distribution is not a probability distribution, give the characteristic which is not satisfied by the distribution.P(X=x)=x+4/15, for x=−5,−4,−3,−2,−1-No, the sum of the probabilities is not equal to 1-Yes, the distribution meets all three properties of a discrete probability distribution-No, one or more of the probabilities do not fall between zero and one.. inclusively-No, the sum of the probabilities is not equal to one and one or more of the probabilities do not fall between zero and one inclusively-No, the probabilities are not additive

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19-12-2022
Mathematics

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Determine whether or not the following distribution is a probability distribution. If the distribution is not a probability distribution, give the characteristic which is not satisfied by the distribution.P(X=x)=x+4/15, for x=−5,−4,−3,−2,−1-No, the sum of the probabilities is not equal to 1-Yes, the distribution meets all three properties of a discrete probability distribution-No, one or more of the probabilities do not fall between zero and one.. inclusively-No, the sum of the probabilities is not equal to one and one or more of the probabilities do not fall between zero and one inclusively-No, the probabilities are not additive

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Qwtiger Qwtiger · Answer 1 · 2022-12-23T06:18:33-05:00

The provided distribution does not meet the requirement that the total of the probabilities of all possibilities must equal one, hence it is not a probability distribution.

The total of the probability in this situation for x=-5, -4, -3, -2, and -1 is (-5 + 4)/15 + (-4 + 4)/15 + (-3 + 4)/15 + (-2 + 4)/15 + (-1 + 4)/15 = -1/3 + 0 + 1/3 + 2/3 + 3/3 = 1/3 + 2/3 + 1 = 4/3, which is not equal to 1. Since the distribution does not represent a probability distribution, it cannot be used.

There is a chance of occurrence for each discrete number that ranges from zero to one. That is not a probability function; it is a discontinuous function that accommodates negative values or values higher than one. Since the probabilities must add up to one, at least a single of the values must be true.

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