題組內容

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

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

(a) \( (5\%) \) Suppose that \( \tilde{X}_k = \sum_{i=1}^{n} X_{ki} \). Find the mean and variance of \( \tilde{X}_k \).