美国统计代写 STA 142A代写

STA 142A: Homework 1

美国统计代写 But copying of the homework constitutes a violation of the UC Davis Code of Academic Conduct and appropriate action will be taken.

• Homework due in Canvas: 01/29 at 11:59PM.
• Please follow the instruction in canvas regarding HWs.
• You are encouraged to discuss about the problems with your classmates.

But copying of the homework constitutes a violation of the UC Davis Code of Academic Conduct and appropriate action will be taken.

1.Question 4 in page 120 of the textbook. (Note: this is an open endedquestion). 美国统计代写 

2.Linear regression simulation. Consider the linear regressionmodel

y_i = β₀ + β₁x_i + s_i, i = 1, . . . , n,

where β₀ = 5, β₁ = 3 and s_i ∼ N (0, 1) and x_i ∼ Uniform(0, 1).

a)Generate n = 100 data points (x_i, y_i) from the above model. Plot the data. Fit alinear regression line model using python and add the fitted line to the plot. You could use the LinearRegression() function from Scikit learn  See documenta-tion at https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html

b)Repeat the experiment in part (a) for 1000 times (without plotting). Note that you willgetdifferent estimates of β₁.  Denote them as βˆ(1), βˆ(2), . . . , βˆ(1000).  What is the mean of these values ?  Plot a histogram of βˆ(1), βˆ(2), . . . , βˆ(1000). 美国统计代写 

c)Repeat (b) but now with s_ibeing  a  standard  Cauchy   How  does  the  histogram change ? Specifically, comment about the tails of histogram. (Note:  Here,  you are still using least-squares linear regression. Only the data generating process is changed.)

3.Question 6 in page 170 of the textbook. 美国统计代写 

4.Bayes Classifter-I. Suppose that Y ∈ {0, 1} and P(Y = 1) = 1/The distribution of

X|Y = 0 is discrete and is specified by

P (X = 1|Y = 0) = 1/3 P (X = 2|Y = 0) = 2/3.

The distribution of X|Y = 1 is discrete and is given by

P (X = 2|Y = 1) = 1/3 P (X = 3|Y = 1) = 2/3. 美国统计代写 

Find the Bayes Classifier (also called as Bayes optimal classification rule).

5. Bayes Classifter-II  Let X  ∈ R correspond to input data and Y  ∈ {+1, −1} correspond  to binary labels. Suppose we assume the following model for the conditional probabilityof Y = 1 given X = x

Let f be a classifier and consider the loss function defined as follows:

What is the decision boundary (value of x) that minimizes the risk? Now suppose we assume the following model for the conditional probability of Y = 1 given X = x

 

What is the decision boundary (value of x) that minimizes the risk?

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