The following density function describes a random variable $X$.

$$f(x) = \frac{x}{36} \;\;\mathrm{if}\;\; 0 < x < 6 \quad\quad\mathrm{and}\quad\quad f(x) = \frac{12-x}{36} \;\;\mathrm{if}\;\; 6 < x < 12.$$

Draw a graph of the density function and then use it to find the probabilities below:

A. Find the probability that $X$ lies between 2 and 5.

Probability =

B. Find the probability that $X$ lies between 3 and 10.

Probability =

C. Find the probability that $X$ is less than 9.

Probability =

D. Find the probability that $X$ is greater than 2.

Probability =