Question: 10. Let X N (1, 2) and Y N (4, 7) be independent random variables. Find the probability of the following events: (a)

10. Let X ∼ N (1, 2) and Y ∼ N (4, 7) be independent random variables. Find the probability of the following events:

(a) X + Y > 0,

(b) X − Y < 2,

(c) 3X + 4Y > 20.

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