Notations to Use in Formulating of Maximum Likelihood Estimation

1. How do you write a maximum likelihood function?
2. What is the maximum likelihood estimator of μ?
3. What is the symbol of likelihood function?

How do you write a maximum likelihood function?

By differentiating and setting the derivative to 0 we obtain ˆθML=n∑nk=1xi. This suggests that the MLE can be written as ˆΘML=n∑nk=1Xi.

What is the maximum likelihood estimator of μ?

Because the second partial derivative with respect to µ is negative, ˆµ(x)=¯x is the maximum likelihood estimator.

What is the symbol of likelihood function?

According to the Wikipedia article Likelihood function, the likelihood function is defined as: L(θ|x)=P(x|θ), with parameters θ and observed data x. This equals p(x|θ) or pθ(x) depending on notation and whether θ is treated as random variable or fixed value.