Some interesting questions Claude cracks: Let W=Q+R where Q and R are standard normal. What is E[Q|W]? Perplexity failed and said W. Both ChatGPT and Claude c

Some interesting questions Claude cracks: Let W=Q+R where Q and R are standard normal. What is E[Q|W]? Perplexity failed and said W. Both ChatGPT and Claude correctly said W/2. Let X(T) be a gaussian process with variance sigma^2 and mean 0. What is E[(e^(X(T)))^2]? ChatGPT and Claude both correctly said E[(e^(X(T)))²] = e^(2σ²) I think Claudes solution was better. I then tried it on a probbailtiy question which wasn't well known and it failed miserably.