Generating random numbers with a seed

Quite often, users want to produce the same set of random numbers repeatedly. For example, when a professor is explaining how to estimate the mean, standard deviation, skewness, and kurtosis of a set of random numbers, it is a good idea that students could generate exactly the same values as their instructor. Another example would be that when we are debugging our Python program to simulate a stock's movements, we might prefer to have the same intermediate results. For such cases, we use the scipy.random.seed() function as follows:

>>>import scipy as sp 
>>>sp.random.seed(12345) 
>>>x=sp.random.normal(0,1,20) 
>>>print x[0:5] 
[-0.20470766 0.47894334 -0.51943872 -0.5557303 1.96578057] 
>>>

Here, 12345 is a seed. The value of the seed is not important. The key is that the same seed leads to the same set of random values. The formula for a more general normal distribution is shown here:

Here, f(x) is the...