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so welcome to this video in this video im going to show you how to derive the pdf of the f distribution from the definition of the f distribution as the quotient of two chi-squared random variables so ive taken these formulae from wikipedia so here is the definition of a f random variable this random variable x in terms of two chi-squared random variables so this s1 random variable is chi squared distributed with d1 degrees of freedom and this s2 random variable here is chi squared distributed with d2 degrees of freedom and then this new random variable x which is the quotient of s1 divided by this value d1 over s2 divided by the value d2 this random variable x is then going to be f distributed with d1 and d2 degrees of freedom by definition and what i want to do is ive also got this formula here which is the formula for the pdf of this f random variable x and i want to go from this definition to this thats the aim for this video the aim of this video is not to explain why the f d