# Let 𝑋 be a Log-Normally distributed RV with 𝜇 = 3 and 𝜎 = 2. Determine 𝐸[max(𝑋 − 100, 0)]

See the question above. I am not quite sure, if my result is correct, because I do not have any solutions. I tried with the following formula:

$$E[X] = e^{\mu+\frac{1}{2} \sigma^{2}} \cdot \Phi\left(\frac{\ln \left(\frac{1}{\alpha}\right)+\mu+\sigma^{2}}{\sigma}\right)-\alpha \cdot \Phi\left(\frac{\ln \left(\frac{1}{\alpha}\right)+\mu}{\sigma}\right)$$

What is the correct result?

• Forgot to mention, my result is 24.403 – gvncore Mar 18 at 18:37
• What's $\alpha$? – Glen_b Mar 19 at 6:11
• $\alpha = 100$ (given in title) – gvncore Mar 19 at 7:33
• Thanks; there's a 100 in the title but no indication there that it's $\alpha$ – Glen_b Mar 19 at 9:11