Why does $$-E \left(\frac{1}{2 \sigma^4}- \frac{(X-\mu)^2}{\sigma^6} \right) = \frac{1}{2 \sigma^4}$$
Shouldn't it be $-\frac{1}{2 \sigma^4}$? Note that $X \sim N(\mu, \sigma^2)$.
Why does $$-E \left(\frac{1}{2 \sigma^4}- \frac{(X-\mu)^2}{\sigma^6} \right) = \frac{1}{2 \sigma^4}$$
Shouldn't it be $-\frac{1}{2 \sigma^4}$? Note that $X \sim N(\mu, \sigma^2)$.