Question: Using the convolution formula, show that the sum of two independent standard normal r.v.s is normal with mean 0 and variance 2 (which is consistent

Using the convolution formula, show that the sum of two independent standard normal r.v.’s is normal with mean 0 and variance 2 (which is consistent with Proposition 5). (Advice: First, show that

Completing the square, write normal r.v.’s is normal with mean 0 and variance 2 (which is

and use the change of variables y−x/2 = s/√2.)

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