$\"\"$

The total number of participants in a pie eating contest in a country fair $\"\"$ .

Find the probability by dividing the frequency of each value by the total number of pies.

The probability of the participant $\"\"$ is $\"\"$ .

Similarlly $\"\"$ .

$\"\"$ .

The probability distribution of $\"\"$ is

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Pies eaten , $\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

$\"\"$

Graph :

Graph the probability distribution.

$\"\"$

The mean value is $\"\"$ .

$\"\"$ .

The mean value is $\"\"$ .

On average, the contests eat $\"\"$ pies.

The variance of random variable $\"\"$ is $\"\"$ .

$\"\"$ .

$\"\"$

The variance is $\"\"$ .

The standard deviation is $\"\"$ .

Substitute $\"\"$ .

$\"\"$ .

Therefore, the standard deviation is $\"\"$ .

$\"\"$

The probability distribution of $\"\"$ is

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Pies eaten , $\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

Graph of the probability distribution is.

$\"\"$

The mean value of a random variable $\"\"$ is $\"\"$ .

On average, the contests eat $\"\"$ pies.

The variance of a random variable $\"\"$ is $\"\"$ .

The standard deviation of a random variable $\"\"$ is $\"\"$ .