Consider an investment with initial capital $2 000. The future value of this investment is random, denote it by X in thousand of dollars. We know the density function of X, which is the following

ct, 0 t 1,

c, 1 t 2,

-ct + 3c, 2 t 3,

0, otherwise.

(a) What is the probability that the investment will be profitable?

(b) What is the expectation of X?

(c) Based on these, should you invest money into this investment, or not?