Prove that the maximum likelihood estimator of the variance of a Gaussian variable is biased.

1. Consider a general optimization problem of the form max

2. Prove that the maximum likelihood estimator of the variance of a Gaussian variable is biased.

3. Regularization for Maximum Likelihood: Consider the following regularized loss minimization: 1 m _m i=1 log(1/ θ [xi ])+ 1 m _ log(1)+log(1/(1−θ)) _

. _ Show that the preceding objective is equivalent to the usual empirical error had we added two pseudoexamples to the training set. Conclude that the regularized maximum likelihood estimator would be

. _ Derive a high probability bound on |ˆθ θ_|. Hint: Rewrite this as |ˆθ −E[ˆθ ]+ E[ˆθ ]−θ_| and then use the triangle inequality and Hoeffding inequality. _ Use this to bound the true risk. Hint: Use the fact that now ˆθ ≥ 1 m+2 to relate

find the cost of your paper

discuss supply and demand along with price elasticity of demand .

I am working on part two of my paper for microeconomics. It is due this evening (11/26/17) by 9:00 MST. The document will need to be about the company of….

Include at least 250 words in your posting and at least 250 words in your reply.  Indicate at least one source or reference in your original post. Please see syllabus for details on submission requirements.

Module 5 Discussion Forum Include at least 250 words in your posting and at least 250 words in your reply.  Indicate at least one source or reference in your original post. Please….

send a copy of the files over an internet platform to an offsite server.

Back up strategies Back up strategy is the planned and well-organized data protection using a backup policy that authorizes the backup responsibilities to the most appropriate and right persons or….