題組內容

3.(30%) Let Ye= 1,2,...n, bei.i.d discrete uniform distribution on {1,2,3,4}. And let

\[ X_{ki} = \begin{cases} 1, \text{if} \quad Y_i = k \\ 0, \text{if} \quad Y_i \neq k \end{cases} \quad \text{for } k = 1, 2, 3, 4. \]

(d) \( (10\%) \) Let \( Z_{1} = \tilde{X}_{1} + \tilde{X}_{2}, Z_{2} = \tilde{X}_{3} \) and \( Z_{3} = \tilde{X}_{4} \). Find the joint distribution of \( (Z_{1}, Z_{2}, Z_{3}) \).