Which of the following represents a valid probability distribution?

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Question:

Which of the following represents a valid probability distribution?Probability
Distribution A
X
P(x)
olo
Probability

Answer:

The option that shows a valid distribution is the probability distribution in option A.

Why is this a valid probability distribution?

In a probability distribution, all the probabilities given must add up to 1.

Of the given functions, only the distribution in A has that quality:

Distribution A:                                                         Distribution B:

= 0.45 + 0.16 + 0.39                                                = -0.14 + 0.6 + 0.25 + 0.29

= 1                                                                             = 1 but probability can’t be

                                                                                    negative

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Distribution C:                                                         Distribution D:

= 0.45 + 1.23 – 0.87 +0.19                                      = 0.87 + 0.56 + 1.38

= 1 but probabililty can’t be negative                    = 2.81

In conclusion, option A is correct.

A 2-column table labeled Probability Distribution B has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled P (x) with entries 0, 0.45, 0.16, 0.39.

The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled P (x) with entries negative 0.14, 0.6, 0.25, 0.29.

A 2-column table labeled Probability Distribution C has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled P (x) with entries 0.45, 1.23, negative 0.87, 0.19.

A 2-column table labeled Probability Distribution D has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled P (x) with entries 0.87, 0.56, 0, 1.38.

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