Question: Let X n and Y n be p-dimensional random vectors such that X n and Y n are independent for each n and their mgfs

Let Xn and Yn be p-dimensional random vectors such that Xn and Yn are independent for each n and their mgfs exist. Show that if

XnDX and YDY,

where X and Y are p-dimensional random vectors, then (Xn, Yn) D→ (X,Y).

XnDX and YDY,

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