Welcome to Excel 2013 statistical analysis,
video number 35.
If you want to download this workbook and follow along,
then this is the second workbook for chapter 5.
Click on the link below the video.
Hey, we've got to talk about the hypergeometric distribution.
Now, we already saw the HYPEGEOM.DIST function
last chapter when we talked about cards and pulling cards,
and the sample space has changed.
Events are not independent.
But here, let's talk about it here in this chapter,
because we can use the function and use
the 0 for probability mask, which
is the probability or the heighth of the column.
And we can use one for cumulative.
Hey, the geometric distribution is
similar to the binomial distribution,
except the trials are not independent.
Remember, when we pull a queen and we
try to get a second queen, well, the sample space has changed.
Instead of 52 cards, there's 51.
And the probability of success changes from trial to trial.
We talked all about conditional probability last chapter.
Here's the function we're going to use,
and this list will translate x.
That's the number of successes.
That's going to show up in our function as sample successes.
Number of trials, n, that's going to be number_sample
So in our card point example, if we wanted two queens in three
tries, sample success would be 2 number
and the sample would be 3.
Number of successes in the population, that's
population_s for successes.
Hey, well, if there is four queens in the deck,
that's that number.
Population size, number_pop.
That's going to be all of the cards, so 52.
And then cumulative, we used 0 last time,
we can use 1 this time.
Now here's our example.
Now two face cards in five tries.
Now last chapter, we actually calculated two queens in three
tries, and we listed all the sample points, then
did our multiplying and adding rule, right.
Well, this one, that's a huge sample space.
I used the combine function to calculate 10,
and oh my heavens, there's 10 of them.
I had to do all of these calculations.
That made my head hurt trying to do all that.
Well, guess what?
The HYPERGEOM.DIST will help us out.
Before we do that, Alt Equals, and let's
just add all these up.
Oh my heavens, I wouldn't like to calculate it that way.
Enter.
So that's a probability of pulling two face
cards in five tries.
Now, the HYPERGEOM.DIST functions equals hypg Tab,
and our sample successes were trying to pull two face cards.
Those are our successes.
Comma, number in the sample, that's
how many trials or steps or cards we're pulling, five.
Comma, population successes, there are 12 total face cards,
not including aces, comma number_pop, that's
all the cards in the decks.
Comma and cumulative, we're using
probability mass, so 0 close parentheses and Control Enter.
That is much easier.
Now, let's go over to the sheet, H2,
because what's nice about this is now
we can list all of our x's for this particular experiment.
Remember, we're pulling five cards.
What's the probability we get zero face cards?
1, 2, 3, 4 and 5 equals hypg Tab.
Our sample successes, there's our random variable,
x for this experiment, comma, number in the sample.
I got a 5 up here, F4, comma, population successes.
There are 12.
F4, comma, and finally the number_pop, F4, comma,
and we want 0 for the actual probability
or heighth of the column.
And I could copy it down.
Alt Equals and Enter.
So there's our 1.
Now let's try probability of x less than or equal to 2.
That means we will have the probability
of pulling 2 face cards, 1 face card or a 0,
adding them all up.
So alt equals 0, 1, and 2, but we have the 1 in our arsenal
when we have our distribution function.
So piper geometric distribution, the number
of successes we want to pull, 2, comma, within 5.
That's our sample.
Population successes, there's 12 face cards,
comma number in the population, 52, comma and 1.
Remember, the 1 always goes from the smallest up to whatever x
we put in.
So close parentheses and enter.
There you go.
Now let's look at another example, example 3.
During the financial crisis of 2008, of the 10 biggest banks,
only three increased lending after they were given TARP
funds of about $2 billion.
Now remember, the TARP funds of $2 billion
were given to the banks in hopes that they would lend money
to people who had good ideas, that
could stimulate the economy, but that just didn't happen.
So here's our experiment.
If you took a random sample of four of the 10 biggest banks
at that time, what is the probability that one of them
would increase lending, all three?
Now the trick is here is we need to know the population size.
That's all the big banks.
Successes in the population, there
was three that actually increased lending.
Sample size is 4, an a success is, did you lend.
So we're going to define our x, our random variable,
as number that did lend in the sample.
So let's go ahead and use our =HYPERGEOM.DIST,
our samples successes, 1, comma the number in the sample,
we're pulling 4.
We're not pulling cards.
We're going out and randomly selecting,
which is like pulling F4, comma, population successes.
There were three banks that increased lending.
F4.
comma, and number, that's the population size, F4, comma, 0,
close parentheses.
Control Enter.
Wow, so if the probability of going out and selecting
four banks and finding one of those four increased lending
was 50%.
I copy this down.
The chance that three of the four was 3 and 1/3 percent.
All right, so in this video, we talked
about the geometric distribution function.
This is for when the sample space is changed.
Oh, by the way, if you do this crazy one over here, right,
we did that last chapter, but we're not
going to do that anymore, because we
want to go ahead and use the Hypergeometric Distribution
function.
We saw how to use a 1, which we didn't do last chapter.
We saw how to add them all up, build the distribution.
All right, so this is the last video for chapter 5.
Next chapter, we get to talk about
continuous random variables.
And we'll get up to start our conversation about the bell
shaped distribution, all right.
We'll see you next video.