00:01
For the given f of x, we have to calculate the cumulative distribution function capital f of x which is given by the formula p of x less than or equal to x.
00:11
Here the range is given such that it is in the form minus infinity to infinity and our range is 0, 1, 2, 3, 4.
00:24
Our range defined only in this region and here this region.
00:30
So we have to calculate capital f of x in this region only.
00:34
So if x less than 1 which is less than lower limit capital fx of x is equal to 0 because small f of x is not defined and when 1 less than or equal to x less than 2 which means that if x is somewhere here we can define capital f of x as integral 1 to x the f of x dx and in this region f of x is defined as 1 by 2.
01:08
So this is it is like this.
01:10
So 1 by 2 is a constant and taking that integrating x is there.
01:15
So this is equal to 1 by 2 into x minus 1.
01:18
So in this range the capital f of x is obtained as 1 by 2 in x minus 1 and in the next limit that is from 2 to 3 if 2 is included and 3 is not included in this case you can see that capital f of x will be from this range is to be completely integrated and here you can see that there is no pdf is defined here.
01:44
So this will be 0 which means that the integration this will be 1 to 2 f of x dx only which means that 1 by 2 x x and the range is from 1 to 2.
02:06
So applying we have this is equal to 1 by 2.
02:10
Now in the next limit 3 less than or equal to x less than 4 capital f of x is defined such that from 1 to 2 f of x dx plus 2 to 3 f of x dx plus 3 to x f of x dx.
02:40
This term will completely turns into 0.
02:45
The first term it is equal to 1 by 2 and the last term we can see that this is equal to 3 to x 1 by 2 p x.
02:56
So this is equal to 1 by 2 plus 1 by 2 into applying the limit this will be x minus 3.
03:04
If we want we can take that 1 by 2 commonly out there...