00:01
So today we're looking at a chi -squared distributed random variable, we'll call it x, and it's got 23 degrees of freedom, so it's 23 degrees.
00:09
And we're going to ask some questions about it.
00:12
So the first thing we're going to do is find the probability that x is between 14 .5 and 32 .01.
00:24
Now, one thing to note about the chi -squared distribution is it's right -skewed.
00:32
There's this tail on the right side, and a lot of times when you look at a table it gives you the right tailed probability.
00:39
So that means, so here's is the following.
00:42
So let's say you have your 14 .5 here and 32 .01 and let me show you what you get.
00:50
So if you look those up in a table and i've used this excel spreadsheet function chi dist where you input the chi squared value and then you use the freedom, you get these values.
00:59
So what do these numbers mean? so if you look at the 32 .01, this you get 0 .099.
01:06
What that means is everything to the right of that value, the area to the right of it, is that value.
01:12
It's a right tail distribution 0 .0.
01:16
You can probably, you know, just for simplicity's sake let's call it 0.
01:20
And then if we look at the 14 value, it's 0 .89.
01:26
So this is what, 0 .9? so that means everything from here on down, including all this stuff is 0 .9.
01:41
So what we do is we take the probability that x is greater than 14 .85 and subtract the probability that x is greater than 32 .01 and that's going to give us this area in between.
02:06
So we get 0 .9 minus 0 .1, 0 .8.
02:14
Great.
02:15
Now for the next part, we're going to find the constants such that the probability of x being between a and b is equal to 0 .95.
02:29
So kind of looking on that same view, this is this, let's clear this up here.
02:36
What we want is is the, have the values a and b.
02:50
B says that the x between them is 0 .95, so this area between them is 0 .95.
03:02
And we're told that the probability of x being less than a is equal to 0 .025.
03:17
So x less than a is 0 .025, and then what that means is this area and i'm going to show you when i show you the answer it's gonna be a mistake and that's the point i want to show you what the mistake is so x less than a is 0 .025 this is not the scale because this area here again it's not the scale this is 0 .025 so that's one thing to note and then what what that means, if this is 0 .025, this up here is also 0 .025.
04:08
So what this means is that when we take a, we actually need to...
04:22
Let me just show you what the mistake is...