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.

(a) \( (5\%) \) Compute \( P[X_3 > X_1 + X_2] \), where \( \sqrt{2} = 1.414 \), \( \sqrt{3} = 1.732 \), \( \sqrt{7} = 2.646 \), \( \sqrt{11} = 3.167 \).