Question
Version:0.9 StartHTML:0000000105 EndHTML:0000008755 StartFragment:0000000141 EndFragment:0000008715 Suppose Y 1 and Y 2 are independent normal distribution with the same variance . Defifine U 1 = Y
Version:0.9 StartHTML:0000000105 EndHTML:0000008755 StartFragment:0000000141 EndFragment:0000008715 Suppose Y1 and Y2 are independent normal distribution with the same variance. Defifine U1 = Y1 + Y2,
U2 = Y1 Y2
a. Show U1 and U2 are joint normal
b. Show U1 and U2 are indenpendent
Hint:
If Y1 and Y2 are independent, they are joint normal such that (Y1, Y2) N2.
Use the results on page 6 and 8 from note 19: in order to show U1 and U2 are joint normal, you
need to show 1. their marginal distributions are both normal; 2. Any linear combination of U1 and
U2, cU1 + cU2 is still normal
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