4. (10%) Let $$L(\sigma) = \prod_{i=1}^n \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{1}{2}\left(\frac{x_i - \mu}{\sigma}\right)^2}, \quad \sigma > 0$$ Where $\mu$ and $x_i, i = 1, 2, \dots, n$ are known values. Find the value of $\sigma$ at which $L(\sigma)$ has its maximum. (Skip any derivative test)

阿摩線上測驗 · 2026-10-22T13:51:09+08:00

4. (10%) Let L(σ) = _i=1^n 1√2πσ e^-1/2((x_i - μ)/σ)^2, σ > 0 Where μ and x_i, i = 1, 2, , n are known values. Find the value of σ at which L(σ) has its maximum. (Skip any derivative test)

4. (10%) Let $$L(\sigma) = \prod_{i=1}^n \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{1}{2}\left(\frac{x_i - \mu}{\sigma}\right)^2}, \quad \sigma > 0$$ Where $\mu$ and $x_i, i = 1, 2, \dots, n$ are known values. Find the value of $\sigma$ at which $L(\sigma)$ has its maximum. (Skip any derivative test)

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