Problem.
Consider the following function

 c,
− c t + 2c,
f (t) =
 2
0,
(i) Find the value of the parameter
random variable
c,
such that
X.
(ii) What is the probability that
(iii) What is the expectation of
X
X?
is less than 2?
0 ≤ t ≤ 2,
2 ≤ t ≤ 4,
otherwise.
f
is a density function of some continuous