(Accuracy) Let a continuous random variable X have probability density func- -2x +ce, x>0 tion f(x)...

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(Accuracy) Let a continuous random variable X have probability density func- -2x +ce, x>0 tion f(x) = | 0, x < 0 (a) Find the value of c that makes f a density. (b) Find the moment generating function for f. (c) Find the expected value and variance of f using the moment generating function. (d) Find the expected value and variance of f directly using the integral definition. Which is easier? (Accuracy) Let a continuous random variable X have probability density func- -2x +ce, x>0 tion f(x) = | 0, x < 0 (a) Find the value of c that makes f a density. (b) Find the moment generating function for f. (c) Find the expected value and variance of f using the moment generating function. (d) Find the expected value and variance of f directly using the integral definition. Which is easier?