00:01
All right, so we have a discrete random variable x with a probability mass function in here and i put it into a spreadsheet to make it into a a table form so it's easy for us to read and then we're also going to make the plot of p of x for all x in the range so x is go from one to five and it's discrete so it's only the integer is one through five inclusive and here it is one two three four five on the x axis p of x and sometimes you might see this has vertical lines going up because it's discrete.
00:38
My program just does bars.
00:41
And the height is the probability.
00:46
Now i'm going to compute and plot the cumulative distribution function f of x.
00:52
So what that is, as you take, it's the sum of everything up to that value.
00:57
The sum of all the p of x up to that x.
01:00
So one, the cumulative is 0 .1.
01:04
2, the cumulative is 0 .1 plus 0 .3.
01:08
3, the cumulative is 0 .1 plus 0 .3 plus 0 .3.
01:13
And you go on the line.
01:17
And then up to 4, you get 0 .9.
01:20
And then the last, we get to 5, it's 1.
01:27
And so you do the same thing, x and the f of x, and that's this graph here.
01:32
And you can see where the probability, this is saying the probability that x is less than equal to 5 is 1.
01:43
And that's what each of these bars is.
01:46
It's the probability of x less than that x, that specific x value, is the height of each bar.
01:55
So there we go.
01:57
Now we're going to compute c and d.
01:59
Now these are actually the same.
02:01
These less than equal to values would be important if it could be that value.
02:13
But because we're dealing with 1 .4 and our variable, as discrete.
02:18
1 .4 is between 1 and 2, but we don't have that, so it's actually between 2 and 4.
02:24
So it's right here...