Question: 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.

A random variable X has a mixed distribution whose discrete and continuous parts, f1(x) and f2(x), are given, respectively, by and f(x)= 2(x)= { 0, 1316 x = 0, x = 4,

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.

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

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