Here are some programming challenges to get you ready for the Quiz on Wednesday 6 April. None of the problems on the quiz will be this hard but you may see problems like this on the final exam.

1. Write an expression to compute the sum of the integers from -5 through 15 inclusive using numpy.





2. Write a loop to compute the sum of the integers from -5 through 15 inclusive without using numpy. 




3. Given a numpy vector V, subtract its mean and divide by its standard deviation leaving the result in R. 




4. What famous constant is this code approximating? (try it at the command prompt then work out what it is doing).

import numpy as np

xy = np.random.rand(10000000, 2) * 2 - 1
xy2 = xy ** 2
z = xy2.sum(1)
count = np.sum(z < 1)
est = 4.0 * count / 1e7
print 'estimate is', est