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Let $X_1, X_2, ..., X_n$ be a random sample from $N(\theta+2, \theta^2)$. Find the MLE of $\theta$. I went through some work and I could not solve for $\theta$. Am I doing anything wrong? $$L( \theta )= \prod _ { i = 1 } ^ { n } \frac { 1 } { \theta \sqrt { 2 \pi } } \exp \bigg[- \frac{( x _ { i ... Julia is a high-level, general-purpose dynamic programming language, most commonly used for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism and the use of multiple dispatch as a core programming paradigm, efficient garbage collection, and a just-in-time (JIT) compiler (with support for ahead-of-time compilation). Julia can be run similar to (interpreted) scripting languages (i.e. Julia has a REPL), and does by default using its runtime (when preinstalled), but Julia programs/source code can also optionally be... 13 hours later… 12:59 PM 2 Let X_1, X_2, ..., X_n be a random sample from N(\theta+2, \theta^2). Find the MLE of \theta. I went through some work and I could not solve for \theta. Am I doing anything wrong?$$L( \theta )= \prod _ { i = 1 } ^ { n } \frac { 1 } { \theta \sqrt { 2 \pi } } \exp \bigg[- \frac{( x _ { i ...

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I have a log-sum-exp expression which I have to minimize as following: $f_\mu(x) = \frac{1}{\mu}log(\sum \exp (\mu(a_j^Tx - b_j))$ where $x \in R^n$, other constants are randomly chosen, and $\mu > 0$ is a given input parameter. The minimization method to employ is the "Analytic center cutting pl...

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