Greetings,

Suppose I have two linear combinations of values as follows:

Y1 = B11*X1 + B12*X2 + B13*X3

Y2 = B21*X1 + B22*X2 + B23*X3

where X1 ~ N(0,1) and X2 ~N(0,1) and X3 ~N(0,1)

Can corrY1,Y2 be derived analytically, that is, without me simulating numerous instances of Y1 and Y2 and doing statistical analysis? if so, I would very much appreciate a demonstration of how that is done, or perhaps a concrete reference to a demonstrated solution.

Suppose I have two linear combinations of values as follows:

Y1 = B11*X1 + B12*X2 + B13*X3

Y2 = B21*X1 + B22*X2 + B23*X3

where X1 ~ N(0,1) and X2 ~N(0,1) and X3 ~N(0,1)

Can corrY1,Y2 be derived analytically, that is, without me simulating numerous instances of Y1 and Y2 and doing statistical analysis? if so, I would very much appreciate a demonstration of how that is done, or perhaps a concrete reference to a demonstrated solution.

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