Graphing basketball binomial distribution

0:00- 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?

0:15Draw 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.

0:31So 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.

0:57So 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.

1:29So 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.

2:05And 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.

2:19So, 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.

2:44So 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.

3:20So 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.

4:03And 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.