Question: If X is normally distributed with mean 50 and variance 100, Y is normally distributed with mean 80 and variance 25, Z is normally distributed

If X is normally distributed with mean 50 and variance 100, Y is normally distributed with mean 80 and variance 25, Z is normally distributed with mean 100 and variance 144, and X, Y, and Z are independent, find the dis¬

tribution of:

(a) X — Y

(c) 6Z + 4X-30F

(b) X+Y-Z

(d) (X+Y + Z)/3.

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