Define a new random variable by y = 2px. show that, as p l 0, the mgf of y converges to that of a chi squared random variable with 2r degrees of freedom by showing that

The moment generating function (mgf) of y is given by



Since the momoent generating function of x is given by

When p tends to 0, we have



Applying L'Hopital's rule we have:



This shows that y converges to a chi squared random variable with 2r degrees of freedom.