00:01
So we are given that a manufacturer goes through the process of piston rings produce whose diameter is in centimeter.
00:12
So, given by the function of f of x is equals to 3 into the bracket 1 minus 16 x minus of 10 whole square when x is varying between 9 .75 to 10 .25 and otherwise it will be 0.
00:36
So, in the first part, we just have to compute the cumulative distribution function of piston ring diameters.
00:45
So, let us get started with solution.
00:48
So, basically we remember that for a part.
00:50
We can define the distribution function is nothing but as mean of the diameter mu of x.
00:58
And that should be equals to integral of negative of infinity to positive of infinity x into f of x dx.
01:08
So let's plug in the values.
01:10
So mu of x is equals to integral.
01:14
Now it is varying for 9 .75...