00:01
In this video, we are going to focus on proving that if t is having a t distribution, so let us write over here as such, and here in this very distribution, the degrees of freedom is equal to v.
00:14
So, if it is true, that is if this condition is true, then x is equal to t square will have f distribution with v1 as equals to 1 and v2 as equals to v degrees of freedom.
00:26
So that has to be proved over here.
00:28
So, firstly, we can consider here pdf of f distribution and it will be here we can write.
00:35
It is basically probability distribution function of f distribution with v1 comma v2 and then it will be like this.
00:46
And now we can say that f of capital f and that is equal to v1 divided by v2 and then it will be here raised to the power v1 divided by 2.
00:58
And in the denominator we are going to have b and then it will be here b1 divided by 2 and v2 divide by 2.
01:07
So it will be here multiplied with f raised to the power v1 divided by 2 and then it is here minus 1 and then it will be here we can say in the denominator we are going to have 1 plus v1 divide by v2 and then it is here multiplied with f.
01:26
So it will be here raised to the power v1 plus v2 divided by 2.
01:32
And now we can say that let us take the value of v1 to be equals to.
01:39
So let us write that v1 values taken as 1 and v2 value is taken as v.
01:45
And thus it can be here said that t square is here equals to f.
01:52
And now we can say that this very value is basically greater than equals to 2t d t and then here it will be equals to df...