Question

Which table is a probability distribution table?

Responses

X 1 2 3 4
P 0.2 0.35 0.15 0.25



X 1 2 3 4 P 0.2 0.35 0.15 0.25 ,

X 1 2 3 4
P 0.4 0.15 0.25 0.2
X 1 2 3 4 P 0.4 0.15 0.25 0.2

X 1 2 3 4
P 0.4 1.05 0.02 0.35
X 1 2 3 4 P 0.4 1.05 0.02 0.35

X 1 2 3 4
P −0.2 −0.1 0.4 0.3

Answer 1

Considering that it has only positive probabilities, and the sum of the probabilities is of 1, the table that shows a probability distribution is given by:

X 0 1 2 3

P 0.1 0.5 0.3 0.1

When does a table represent a probability distribution?

A table is formed by a set of points (x, P(x)), and represents a probability distribution if:

The sum of the probabilities is of 1.

All probabilities are 0 or positive.

In this problem:

In the first table, there is a negative probability, which is P(X = 0) = -0.3.

In the second and the fourth tables, the sums are of 1.2 and 0.8, respectively.

Hence, the table that represents a probability distribution is given as follows:

X 0 1 2 3

P 0.1 0.5 0.3 0.1