2. (15 pts) Let

4 x 0 x 1 2

f(x)= 44x 12x1 0 otherwise.

1. (a)(3 pts) Plot the graph of f(x). Make sure to label your plot, carefully identifying some of the important points on the graph of f(x).
2. (b)(5 pts) Is f(x) a density function for a continuous random variable X? (Note: You need to check two conditions).
3. (c)(7 pts) Calculate the expected value E(X) and the variance V (X). Make sure you show all the appropriate calculations and explanations for your answer.