Question

Customers at TAB are charged for the amount of salad the take. Sampling suggests that the

amount of salad taken is uniformly distributed between 5 ounces and 15 ounces. Let

Χ = Salad plate filling weight.

i. Find the probability density function of Χ

Answer 1

The probability density function of X is:

`f_(X)(x)=(1)/(15-5)=(1)/(10);\ 5<X<15`

Explanation:

A continuous Uniform distribution is the probability distribution of a random outcome of an experiment that lies with certain specific bounds.

Consider that random variable X follows a continuous Uniform distribution and the value of X lies between a and b.

The probability density function of the random variable X is:

`f_(X)(x)=(1)/(b-a);\ a<X<b,\ a<b`

Now, in this case it is provided that the amount of salad taken is uniformly distributed between 5 ounces and 15 ounces.

The random variable X is defined as:

Χ = Salad plate filling weight.

The probability density function of the salad plate filling weight is:

`f_(X)(x)=(1)/(15-5)=(1)/(10);\ 5<X<15`