The discussion focuses on calculating the expected values E(Z^3) and E(Z^4) for a standard normal distribution where Z has a mean (μ) of 0 and a standard deviation (σ) of 1. The probability density function is defined as f(z) = e^(-z^2/2)/sqrt(2π). The user attempted to compute these expected values using integrals from -∞ to ∞, specifically ∫Z^3 * f(z) dz and ∫Z^4 * f(z) dz, but expressed uncertainty about the correctness of their approach.
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whitedragonxx said:Homework Statement
Let Z follow a standard normal distribution. Compute E(Z^3) and E(Z^4)
Homework Equations
I know that mu is 0 and sigma is 1. And f(z) = e^(-z^2/2)/sqrt(2pi)
The Attempt at a Solution
I tried to take the integral of ∫Z^3 * f(z) from the integral from -∞ to ∞
and did the same for E(Z^4) where the Z^3 is replaced by Z^4, but I don't know if I am doing the problem right or wrong.