承接返之前就An introduction to Quantitative Finance問過嘅問題
當中有一條問題係
Evaluate `E(max{K-X,0})` where `X~N(mu,sigma^2)` and `K` is a constant.
Hint: Use `K-X=(K-mu) - (X-mu)`

我用以下嘅方法計但係simplify唔到

`E(max{K-X,0})`
`=int_{-oo}^{oo} max{K-x,0}f(x)"d"x`
`=int_{-oo}^{K} (K-x)f(x)"d"x + int_{K}^{oo} 0 cdot f(x)"d"x`
`=int_{-oo}^{K} (K-mu)f(x)"d"x - int_{-oo}^{K} (x-mu)f(x)"d"x`
`=(K-mu)Phi(K) - int_{-oo}^{K} (x-mu)f(x)"d"x`

可唔可以幫手睇下點做？