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SOLVED:Let the random variable Z have the standard normal distribution. (a) Verify that the probability density function of |Z| is given by √(2 / π) e^-(1)/(2) z^2 for z>0 with E(|Z|)=√(2 / π) and σ(|Z|)=√(1-2 / π). (b) Use the formula for the expected value in Problem 4.26 to verify that E[max(Z-c, 0)]=(1)/(√(2 π)) e^-(1)/(2) c^2-c[1-Φ(c)] for any c ≥0.
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