Append your code at the end of the report. DO NOT paste an image of the code. The code must be in the form of text in the PDF file - not an image. Cross Valida- tion and Ridge Regression must be your own implementation. You are not allowed to use external libraries for implementing Cross Validation and Ridge Regression. For e.g., if you are using Python, you may use numpy and numpy.linalg. But, you are NOT allowed to use a library like sklearn.linear_model.Ridge or sklearn.model_selection.cross_val_score. You may use Python libraries like matplotlib for plotting figures.

 

Q.1 20 points Suppose that we have 3 colored boxes r (red), b (blue), and g (green). Box r contains 3 apples, 4 oranges, and 3 limes. Box b contains 1 apple, and 1 orange. Box 9 contains 3 apples, 3 oranges, and 4 limes. If a box is chosen at random with probabilities p(r) = 0.2, p(b) = 0.2, and p(g) = 0.6, and a fruit is removed from the box (equal probability of selecting any fruit in the box), what is the probability of selecting an apple? If the selected fruit is an orange, what is the probability that it came from the green box? Q.2 20 points Daily maximum temperature in Atlanta in Summer is assumed to be from a normal distribution p(t) = 1 22 1 202 exp{2- (t )}. If m temperatures are observed, show that the Maximum Likelihood estimates of the mean and variance are ML = 1 m t(), and L m = ML m 1=(t() - HML)2, respectively.