Question: 8. Two normal random variables. Let X , Y be i.i.d N(0, 02) random variables and c > 0 a positive real number. (a) (3

8. Two normal random variables. Let X , Y be i.i.d N(0, 02) random variables and c > 0 a positive real number. (a) (3 pts) Argue that any linear combination aX + [31' for a, ,6 6 IR is normally distributed. (b) (2 pts) Draw the region in the place corresponding to the event {X Z 0, Y 3 CK}. (c) (5 pts) Using the symmetries of (X , Y), deduce a formula for ]P(X > 0, Y

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