00:01
We're told we have a random variable x with a mean mu of 8 and a variance of square of 9.
00:08
And we don't know the probability distribution.
00:10
We don't know what the distribution is.
00:12
But we don't find some probabilities.
00:14
We don't find the probability that x is between negative 4 and 20.
00:19
And this is a convenient set of numbers, negative 4 and 20, because 8 falls right in the middle of them.
00:24
We think about negative 4.
00:27
Here's negative 4.
00:30
Here's roughly 20 right here.
00:34
Well, 8 is going to be right in the middle.
00:36
And the difference between 8 and 20 is 12, and the difference between negative 4 and 8 is also 12.
00:43
So what we're really looking at is the difference we're going to be within 12.
00:52
That's what we're saying.
00:52
We're going to be within 12 units.
00:54
So in other words, we're going to find the probability that the absolute value of x minus 8 is less than 12.
01:05
And this is a perfect setup for check.
01:10
Mbby chb's rule, which says the following.
01:12
And this, i'll put us in a different, separate color.
01:16
So it says the probability, the absolute value of x minus mu is less than k sigma is greater than 1 minus 1 over k squared.
01:36
And that's what we're saying...