00:01
We're looking at tsunamis, and we know that 30 % are 9 meters or higher.
00:07
So pick a random earthquake that produces a tsunami, and p is 0 .3, it'll be 9 meters or higher.
00:15
We're looking at a sample of size 6.
00:18
Okay, so first we need a histogram of the probability distribution, and then we're going to get some notes.
00:27
Okay.
00:27
Okay.
00:30
So here we have a binomial distribution because we have a series of independent frills, each earthquake, and each one has two outcomes.
00:40
The tsunami is over nine meters, or something else happens.
00:44
And the probabilities are the same for each, because we're looking at a rate.
00:50
So to make a histogram, we're going to need the x -axis.
00:57
That's going to be x the number of tsunamis nine meters or higher.
01:02
Actually it gives us a variable r so r is going to be on x -axis and on the y we have the probability of that many being nine meters or higher.
01:14
To actually get the heights of our bars here we're going to use the binomial formula which is the probability of r is n choose r p to the r, 1 minus p, n minus r.
01:32
So this is the binomial formula.
01:34
With these three terms we multiply together.
01:37
And if i start with, let's say, 3, r equals 3, what we're saying is we have three of them that are 9 metres or higher, and 3 that are not.
01:48
So this term is the probability of three of them being 9 meters or higher.
01:55
This is the probability of three of them not being so.
01:58
And this is the number of ways you can put these events in order.
02:03
This is just one order.
02:05
And these two terms alone only get one particular case.
02:09
But this is a different order.
02:12
So i need to take that into account.
02:15
I'm just going to lose my graph.
02:27
So for an example, i'll use three.
02:30
It's going to be, so this is called six choose three, is 20.
02:40
Times 0 .3 to power of 3 times 0 .7 to power up 3.
02:45
Most calculators just have a button like this.
02:47
If not, it's a combination problem.
02:49
N factorial over r factorial times n minus r factorial.
02:57
Just calculate this.
03:02
And this is 0 .18522.
03:06
And it's not going to be the highest bar, i don't think, but pretty high.
03:13
So you would repeat this process.
03:18
For each and draw out the bars.
03:21
So i'm going to make some, let's say we have, 0, 1, 2, 3, 4, 5 and 6.
03:30
And, okay, so the highest probability we have to deal with is about 0 .32, so i'll have point 1, 0 .2 and 0 .3.
03:48
Okay, so i'm going to make some dots to represent these.
03:51
We've already calculated three as being 0 .185.
03:57
So that'll be about here...