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 ...

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 ...

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...