d. Let X and Y be independent normal random variables, each with mean µ and standard deviation o. 1. Consider the random quantities X + Y and X – Y. Find the moment generating function of X + Y and the moment generating function of X –Y. 2. Find the joint moment generating function of (X + Y, X – Y). 3. Are X + Y and X – Y independent? Explain your answer using moment generating functions.

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.