# 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

For each , the probability falls between and inclusive, which meets the first property of the probability distribution.

for all x values

Step 8

Find the sum of the probabilities for all the possible values.

Step 9

Step 9.1

Add and .

Step 9.2

Add and .

Step 9.3

Add and .

Step 9.4

Add and .

Step 10

For each , the probability of falls between and inclusive. In addition, the sum of the probabilities for all the possible equals , which means that the table satisfies the two properties of a probability distribution.

The table satisfies the two properties of a probability distribution:

Property 1: for all values

Property 2: