SOLVED: Problem 3 - Characteristic function and moments:A continuous random variable X has the following probability density function:f(x) = Zx for -2 < x < 0 else 0(a) Determine the characteristic function Φ(0) = Ee^(ioX) = ∫f(x)e^(iex) dx;(b) Compute the first two moments using the characteristic function or the probability density function, i.e. EX^k = ∫x^k f(x) dx for k = 1,2;(c) Use the characteristic function or the probability density function to determine the mean and variance of th

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Answered: Identify a function f that has the given characteristics. f(–5) = f(4) = 0; f '(-0.5) = 0, f '(x) < 0 for x < -0.5; f '(x) > 0 for x > -0.5 f(x) = | bartleby