Question: Use a convolution integral to show that if X ~ N(#1, o') and Y ~ N(u2, 02) are independent, then T = X+Y ~ N(#1

Use a convolution integral to show that if X ~ N(#1, o') and Y ~ N(u2, 02) are independent, then T = X+Y ~ N(#1 + 12, 202). You can use a standardization (location-scale) idea to reduce to the standard Normal case before setting up the integral. Hint: complete the square

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