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 cdf F(x), and (iv) find μ and σ2: (a) f(x) = 4xc, 0 ≤ x ≤ 1. (b) f(x) = c √x, 0 ≤ x ≤ 4. (c) f(x) = c/x3/4, 0 < x < 1

(a)

c=1/2

cdf  is    

Step-by-step explanation:

Remember that if    is the pdf of a random variable X .

Then,

(a)

Therefore

c=1/2

and

then to compute the cdf, we have

step-by-step explanation: yes

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