1. How do you implement a custom ufunc in NumPy?

2. How can you use NumPy's broadcasting to perform batch matrix multiplication?

3. How do you perform Singular Value Decomposition (SVD) using NumPy?

4. How do you compute the QR decomposition of a matrix using NumPy?

5. How can you solve a system of linear equations using NumPy?

6. How do you compute the Moore-Penrose pseudo-inverse of a matrix using NumPy?

7. How do you use NumPy's advanced indexing to select and modify specific elements of an array?

8. How do you create a view of an array with different strides using NumPy?

9. How do you compute the Fast Fourier Transform (FFT) of a signal using NumPy?

10. How do you perform convolution operations using NumPy?

11. How can you use NumPy to implement the Hadamard transform?

12. How do you generate random numbers from a specific probability distribution using NumPy?

13. How do you simulate a random walk using NumPy?

14. How can you use NumPy's vectorized operations to implement the k-means clustering algorithm?

15. How do you perform polynomial fitting using NumPy?

16. How do you use NumPy to interpolate missing data in an array?

17. How can you use NumPy to perform numerical integration?

18. How do you solve ordinary differential equations using NumPy?

19. How can you use NumPy to implement the PageRank algorithm?

20. How do you use NumPy to perform Principal Component Analysis (PCA)?

21. How do you use NumPy's memmap to handle large datasets that don't fit into memory?

22. How do you perform element-wise operations on structured arrays in NumPy?

23. How do you use NumPy to calculate the eigenvalues and eigenvectors of a matrix?

24. How do you use NumPy to perform matrix exponentiation?

25. How can you use NumPy to implement a Kalman filter?

26. How do you perform tensor contractions using NumPy?

27. How do you calculate the gradient of a function using NumPy?

28. How do you perform automatic differentiation using NumPy?

29. How do you use NumPy to generate samples from a multivariate normal distribution?

30. How do you use NumPy's einsum function for complex array operations?

31. How do you use NumPy to implement the FastICA algorithm for Independent Component Analysis?

32. How can you use NumPy to perform wavelet transformations?

33. How do you implement the Discrete Cosine Transform (DCT) using NumPy?

34. How do you use NumPy to simulate the Ising model in statistical physics?

35. How do you implement the Monte Carlo method using NumPy?

36. How can you use NumPy to perform sparse matrix operations?

37. How do you use NumPy to compute the Cholesky decomposition of a matrix?

38. How do you perform matrix completion using NumPy?

39. How can you use NumPy to solve the Travelling Salesman Problem?

40. How do you use NumPy to perform linear regression with regularization?

41. How do you use NumPy to implement a genetic algorithm?

42. How can you use NumPy to perform Gibbs sampling in Bayesian inference?

43. How do you use NumPy to implement the Metropolis-Hastings algorithm?

44. How do you perform statistical hypothesis testing using NumPy?

45. How do you use NumPy to perform permutation tests?

46. How do you use NumPy to perform bootstrap resampling?

47. How do you use NumPy to generate Sobol sequences for quasi-random sampling?

48. How can you use NumPy to implement the Viterbi algorithm for Hidden Markov Models?

49. How do you use NumPy to perform ridge regression?

50. How can you use NumPy to implement the Expectation-Maximization (EM) algorithm for Gaussian Mixture Models?