Assignment 1  Sampling distributions

CSCI 362: Machine Learning Assignment 1
 Sampling distributions
The torch function randn can be used to generate normally distributed numbers.
1. Describe in one or two sentences the output of following program.
import torch
xs = torch.randn(30)
print(xs)
Why is the output different each time you run the program?
2. Add lines to the program above that print the mean and standard deviation of the 30 numbers held
in xs. Hint: PyTorch tensors implement methods mean() and std(). Include a screenshot of your
program and its output in your document for this assignment.
ˆ Is the mean exactly equal to zero? If it is not, why not.
ˆ Is the standard deviation exactly equal to one? If it is not, why not.
Write your answers in your document.
3. Modify your program so that it generates and prints 30 numbers from the normal distribution with
mean 100 and standard deviation 25. (Note: we saw in class that there is more than one way to
do this in PyTorch!) Include a screenshot of your program and its output in your document for this
assignment.
4. If you use your program in the last exercise to generate a single sample of size 30, it is highly unlikely
that the mean of the sampled numbers will be exactly 100. In fact, you would routinely get numbers
in the low 90s or around 110.
However, suppose that you draw many samples of size 30; and that for each such sample you compute
and record its mean. What would you expect the mean of those means to be?
Write a program do this and see if your prediction is correct? (Screenshot your code and its output
and include it in your document).
5. Do the same as in the last exercise but for the standard deviation. Does the mean of the standard
deviations over very many samples target the correct value? As always, include your code and its
output.
6. What happens if you sample from the uniform distribution on [0,1] instead of a normal distribution?
What value does the mean of the means of samples of size 30 appear to target? What about the mean
of the standard deviations of many samples of size 30?
Modify your program above, and include screenshots in your solution document.