Question: Suppose that the random variables X1, X2, and X3 are i.i.d., and that each has the standard normal distribution. Also, suppose that Y1 = 0.8X1

Suppose that the random variables X1, X2, and X3 are i.i.d., and that each has the standard normal distribution. Also, suppose that
Y1 = 0.8X1 + 0.6X2,
Y2 = √2(0.3X1 − 0.4X2 − 0.5X3),
Y3 = √2(0.3X1 − 0.4X2 + 0.5X3).
Find the joint distribution of Y1, Y2, and Y3.

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