00:01
Hi, i'm david and i'm here to help the answer your question.
00:04
Now let me bring up your question here.
00:07
In this question we want to discuss about the probability density function on the random variable.
00:14
Here with the density function we can compute the probability easily.
00:21
And here in the question a, we want to find the probability of the y smaller than 3 .2.
00:28
For the continuous random variable, probability equal to the integral and then here y goes from 2 to 4 so that found the minimum limit will be 2 up to the 3 .2 the density will be 1 over 8 y plus 1 dy and to find this probability we will bring the 1 over 8 outside untidy derivative of the y equals y square over 2 and tiny derivative of 1 equals y evaluate from 2 to the 3 .2.
01:03
So get equal to 1 over 8 and the 3 .2 we put in and then we've got the 3 .2 square over 2 plus 3 .2 and then minus if we put the 2 inside we have the 2 square over 2 minus 2 and if we compute this one we have 3 .2 square given by 2 and then plus 3 .2 2 and then minus 4 and devalued 8 equal to the 0 .54.
01:39
Similarly, we will have to find probability of the y between the 2 .9 and the 3 .2.
01:48
So we will have this will be integral from 2 .9 up to the 3 .2.
01:54
So we have 1 over 8 y plus 1, d .y.
01:59
And then we want to evaluate the integral we will have one over eight and tie derivative will be y square over two plus y evaluate from 2 .9 up to the 3 .2 then we have 1 over 8 and then we put the 3 .2 square over 2 plus 3 .2 minus and the 2 point now we have the 2 .9 square over 2 minus 2 .9 then we get equal to 3 .2 square divided by 2, and then plus 3 .2 minus 2 .2 divided by 2 .2 minus 2 .9, divided by 8.
02:51
So equal to the 0 .15, 1875.
02:58
Now for the question b, we want to find the question b.
03:04
Distribution function will be the capture of the fx and by definition the cumulative distribution function just equal to the probability of the random variable x small equal to the small x and just equal to integral from 2 to the x 1 of 8 y plus 1 so this one why so i will turn this on into the y here so everything will be the y small y y y and this will be the y and this will be so we have untie derivative 1 over 8 y square over 2 plus y evaluate from 2 to buy...