 Solution

ID: past-exam-of-the-systems-biology-course-of-the-university-of-cambridge/2024/paper-3/2/a/solution

f (x_{i} ∣ μ) = \frac{1}{2 π} exp [- \frac{1}{2} (x_{i} - μ)^{2}] .

L (μ) = i = 1 \prod n f (x_{i} ∣ μ) = (2 π)^{- n /2} exp [- \frac{1}{2} i = 1 \sum n (x_{i} - μ)^{2}] .

Independence justifies multiplication; the common mean and known unit variance justify using this same density factor for every observation.

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