Welcome to this third lecture on matlab
and probability. In this lecture we're
going stray from your typical
probability course. So we're going to
have some data matrix, and we're going to
measure the probability of a variable
that the data matrix represents. So what
I want you to do is I want you to go to
in your web browser github.com/lazyprogrammer/
matlab-probability-class.
Once you go there, you're going to copy
and paste this SSH clone URL, and I want
you to go into your terminal and type in
and git clone, and then paste that URL.
I've already done it so I'm not going to
do it again. This is going to give you
some files that are relevant to this
class that I'm going to use for the
coming lectures.
Okay, so, now that you have those files
you want to go into matlab, change your
directory to work in that same directory
that you guys checked out from git.
So we're going to load this data. Ok, so, r
is a 100 by 1 matrix, so let's just plot
r amd let's see what it looks like. Alright,
so, it has a bunch of random values that
are between -5 and 5. So now
let's say I wanted to calculate the
probability that r is equal to
-5. How would I do that? So, one way is I
could sum all the values where r is
equal to -5 and divide it by the
total number of values in r. So it
gives me .07. I can do the same
thing for every other value in the
matrix.
So we get about .06
to .11. So this is what we call the
frequentist view of statistics. It means
that if we flip a coin 1000 times, and
that's a fair coin with heads or tails, the probability is 50% and we
should get heads about 500 times, and we
should get tails about 500 times. The
idea is that as the number of coin flips
approaches infinity, our measurement of
the probability of heads should approach
0.5. So we can also plot the histogram
of r, and this should give us an idea
of the shape of the distribution. Alright,
so, let's do a little more complex
example. Let's say I want to calculate
the probability r is even. How can
we do that? So in the same way as we did
before, we might want to say r equals
-4 or r equals -2, but
that wouldn't be the best way to do this.
We would use the modulo function. So if
mod(R,2) is equal to 0, that means r
is even, divided by the length of r.
Alright, so the probability that r is
even is .43, and we can do
the same thing to determine the
probability that r is odd. And so
notice that these two events are
disjoint. You can either have r equals
even or r equals odd, and those two
events are the only possible events. So
their probabilities should add up to 1,
and we can verify that .43 plus
.57 is equal to 1. Now so let's
say I want to test if r takes on a
specific value, so let's say I want to
calculate the probability that r is
equal to -5 or positive 5. How
would I do that? So we would use the or
operator. So r equals 5 or r equals
-5, divided by the length of r.
So the probability that r is equal to 5
or negative 5 is .21. Notice
that we can use the same method for our
first problem which was to determine even or
odd.
Which is the way I suggested not doing
it, but we want to check our answers, and
so that gives us the same answer. The
probability that r is equal to
-4, -2, 0, 2, or 4 is the same as the
probability that r is even.