題組內容

B. Suppose that the random variables $Y_1, Y_2, \ldots, Y_n$ satisfy $$Y_i = \beta x_i + \varepsilon_i, \quad i = 1, 2, \ldots, n,$$ where $x_1, x_2, \ldots, x_n$ are fixed constants, and $\varepsilon_1, \varepsilon_2, \ldots, \varepsilon_n$ are iid $N(0, \sigma^2)$ with $\sigma^2$ unknown.

(a) (7%) Find a two-dimensional sufficient statistic for \( (\beta, \sigma^2) \).