Quote:
Originally Posted by GB449
a) what does selecting independently with P(x) mean? In earlier homework, we selected the points at random from [1,1] which was clear to me  I used a random function with min = 1 and max = +1 but I am not clear what to do with P(x)

In this problem P(x) is the uniform probability distribution on [1,+1] and so what you did in the earlier homework is exactly what this means  generate a random number between 1 and +1. In general, the way to generate
may not be uniformly random over [1,+1]. It is
that specifies the input probability distribution. For example, if
is the Gaussian distribution with mean 0 and variance 1, then you would generate each
from that Gaussian distribution.
Note
. Each
should be an independent Gaussian random number with mean 0 and variance 1 (you then multiply this random number by
).