A random variable X has a mixed distribution whose discrete and continuous parts, f1(x) and f2(x), are given, respectively, by

for some suitable constant c.
(i) What is the range of values for X?
(ii) Find the value of the constant c.
(iii) Calculate the probability P(2 ≤ X ≤ 4).
(iv) Obtain the expectation and variance of X.

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and f(x)= 2(x)= { 0, 1316 x = 0, x = 4, c(x+1) 6 0 < x < 4, elsewhere,