題組內容

I. Answer the following problems related to probability and maximum likelihood methods.
A. Let $X_1, X_2, X_3$ be independent and follow normal distributions N (0, 1), N (3, 4), N (4, 9), respectively.

(b) $ (10\%) $ Use the moment generating function technique to find the joint distribution of $ W_{1} = X_{1} + 2X_{2} + X_{3} $ $W_2 = 2X_1 - X_3$, and $W_3 = -2X_2 + X_3$.

題組內容

(b) \( (10\%) \) Use the moment generating function technique to find the joint distribution of \( W_{1} = X_{1} + 2X_{2} + X_{3} \) $W_2 = 2X_1 - X_3$, and $W_3 = -2X_2 + X_3$.

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