# Statistics Examples

Step 1

A discrete random variable takes a set of separate values (such as , , ...). Its probability distribution assigns a probability to each possible value . For each , the probability falls between and inclusive and the sum of the probabilities for all the possible values equals to .

1. For each , .

2. .

Step 2

is between and inclusive, which meets the first property of the probability distribution.

is between and inclusive

Step 3

is between and inclusive, which meets the first property of the probability distribution.

is between and inclusive

Step 4

is between and inclusive, which meets the first property of the probability distribution.

is between and inclusive

Step 5

is between and inclusive, which meets the first property of the probability distribution.

is between and inclusive

Step 6

is between and inclusive, which meets the first property of the probability distribution.

is between and inclusive

Step 7

is not less than or equal to , which doesn't meet the first property of the probability distribution.

is not less than or equal to

Step 8

is between and inclusive, which meets the first property of the probability distribution.

is between and inclusive

Step 9

The probability does not fall between and inclusive for all values, which does not meet the first property of the probability distribution.

The table does not satisfy the two properties of a probability distribution