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

Suggest a modification of the binary search algorithm that emulates this strategy for a list of names.

1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

Explain why insertion sort works well on partially sorted lists.

1. Which configuration of data in a list causes the smallest number of exchanges in a selection sort? Which configuration of data causes the largest number of exchanges? 2. Explain….

Draw a class diagram that shows the relationships among the classes in this new version of the system

Jack decides to rework the banking system, which already includes the classes BankView, Bank, SavingsAccount, and RestrictedSavingsAccount. He wants to add another class for checking accounts. He sees that savings….