Graphing Basketball Binomial Distribution - Probability and Statistics,

- In the last video, we worked through
essentially the probability distribution
for this random variable defined as
the number of free throws you make
when taking size free throws,
assuming you have a 70
percent free throw percentage,
and I suggested, hey, why
don't you visualize this?
Draw the graph of this
probability distribution,
this binomial probability distribution.
And when I thought about it, I said,
well, I too would enjoy graphing it,
and we might as well do it together,
because whenever you graph these things
it makes it very visual,
and kind of the shape of a
binomial distribution like this.
So let's do that.
So let me maybe move over
to the right a little bit,
I really just need to
be able to keep track
of these things right over here.
Let me draw some lines.
If I were to just draw one line there,
and then another line here,
and then we have the
different percentages.
So let's do that.
See, the highest one is
a little over 32 percent.
So maybe we'll go as
high as 40 percent here.
40 percent, and then
this would be 20 percent.
20, that looks about half way, 20 percent.
This would be 10 percent.
And this would be 30 percent.
And then in this axis, let's
do the different values
that the random variable could take on.
So the random variable taking on
the value zero.
The random variable
taking on the value one.
Zero, one, the random
variable taking on two.
Two, we're almost there.
Let's see, three, and then four.
Four, and then five.
Five, and then finally six.
Take x equals six.
And then six, and now let's
just graph all of these.
So this first one, zero point one percent,
well, that's barely going to register
on this graph right here,
so I'll just kind of
just give it a little bit
of a showing right over there.
Showing (mumbles) due to that green color.
So, let me make sure.
So, in that green color,
you're going to have just
a little bit of a showing.
One, as well, is kind of barely a showing.
So it shows up a little bit more.
So let me draw it like that.
That is one percent, right over there.
Now, two is six percent,
which on this scale,
is going to be about that high.
So let me draw it like that.
So that is two.
So that is six percent right there.
X equaling three, 18
and a half percent shot
of that happening...
So 18 and a half, it's a hand drawn chart,
or histogram, so you have to bear with me.
So it's roughly there, and then four
was 32.4 percent, so that is up here.
So 32.4 percent looks like that.
Let me shade that in, 32.4 percent.
And then five was 30.3 percent,
30.3 percent, slightly
lower, just like that.
And it will look like this.
30.3 percent, and finally,
six is 11.8 percent.
So really, this whole video was just
an exercise in making a histogram,
but it's useful, because
to actually visualize
what the distribution looks like.
And what's really interesting,
is to think about how does this change
as you change the free throw percentage,
or as you change the
number of shots you take,
how does this change this
binomial distribution?
And you can do that on a spreadsheet,
and actually see how that all works out.