For each of the following functions i find the constant c so

For each of the following functions, (i) find the constant c so that f(x) is a pdf of a random variable X, (ii) find the cdf, F(x) = P(X x), (iii) sketch graphs of the pdf f(x) and the distribution function F(x), and (iv) find µ and variance:

(a) f(x) = x³ / 4, 0 < x < c

(c) f(x) = c / x, 0 < x < 1. Is this pdf bounded?

Solution