1. The problem statement, all variables and given/known data Suppose X1, X2, ..., Xn constitute a random sample from a population following N(μ,θ) where μ is known. (a)Find a sufficient statistic for θ. (b)Use the maximum likelihood estimator of θ to construct a confidence interval for θ with confidence level 1-α. 2. Relevant equations 3. The attempt at a solution For part (a), I have tried to use the factorization criterion to find the sufficient statistic for θ but I have difficulty in separating θ from the exponential function as θ is the denominator. Can someone teach me how to get a function that depends on Xi only! For part (b), the maximum likelihood estimator of θ is (1/n)*Σ(Xi-μ)^2. I am not sure about whether the information that Σ(Xi-μ)^2/θ follows chi square distribution with n degrees of freedom can help us to find the confidence interval! Can someone teach me how to get the confidence interval as well?