Your question is Advanced Probability and Optimization. Take a moment with it on the right.
Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).
How would you solve problems involving conditional probability, Bayes theorem, Monte Carlo methods, and gradient descent?
Explain the assumptions, derive the relevant equations, and demonstrate each method with a small numerical example. Show how you would validate the calculations computationally, diagnose convergence or simulation issues, and communicate uncertainty and limitations.