📗 [2 points] There is a total of red or green balls in a bag. How many red balls and how many green balls are there so that the entropy of the color of a randomly selected ball is imized?

📗 Answer (comma separated vector): .

📗 [4 points] There are parrots. They have either a red beak or a black beak. They can either talk or not. Complete the two cells in the following table so that the mutual information (i.e. information gain) between "Beak" and "Talk" is :

📗 Answer (comma separated vector): . Calculate

📗 [4 points] What is the conditional entropy \(H\left(B|A\right)\) for the following set of training examples.

📗 Answer: . Calculate

📗 [4 points] In a problem where each example has real-valued attributes (i.e. features), where each attribute can be split at possible thresholds (i.e. binary splits), to select the best attribute for a decision tree node at depth , where the root is at depth 0, how many conditional entropies must be calculated (at most)?

📗 Answer: . Calculate

📗 [3 points] A hospital trains a decision tree to predict if any given patient has technophobia or not. The training set consists of patients. There are features. The labels are binary. The decision tree is not pruned. What are the smallest and largest possible training set accuracy of the decision tree? Enter two numbers between 0 and 1. Hint: patients with the same features may have different labels.

📗 Answer (comma separated vector): . Calculate

📗 [4 points] You are given a training set of six points and their 2-class classifications (+ or -): (, +), (, +), (, +), (, -), (, -), (, -). What is the decision boundary associated with this training set using 3NN (3 Nearest Neighbor)? Note: there is one more point compared to the question from the homework.

📗 Answer: . Calculate

📗 [4 points] What is the convolution between the image and the filter using zero padding? Remember to flip the filter first.

📗 Answer (matrix with multiple lines, each line is a comma separated vector): . Calculate

📗 [4 points] What is the gradient magnitude of the center element (pixel) of the image . Use the x gradient filter: \(\begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}\), and the y gradient filter: \(\begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix}\). Remember to flip the filters.

📗 Answer: . Calculate

📗 [4 points] In a convolutional neural network, suppose the activation map of a convolution layer is . What is the activation map after a non-overlapping (stride 2) 2 by 2 max-pooling layer?

📗 Answer (matrix with multiple lines, each line is a comma separated vector): . Calculate

📗 [4 points] A convolutional neural network has input image of size x that is connected to a convolutional layer that uses a x filter, zero padding of the image, and a stride of 1. There are activation maps. (Here, zero-padding implies that these activation maps have the same size as the input images.) The convolutional layer is then connected to a pooling layer that uses x max pooling, a stride of (non-overlapping, no padding) of the convolutional layer. The pooling layer is then fully connected to an output layer that contains output units. There are no hidden layers between the pooling layer and the output layer. How many different weights must be learned in this whole network, not including any bias.

📗 Answer: . Calculate

📗 [4 points] What is the gradient magnitude of the center element (pixel) of the image . Use the x gradient filter: \(\begin{bmatrix} -1 & 0 & 1 \end{bmatrix}\), and the y gradient filter: \(\begin{bmatrix} -1 \\ 0 \\ 1 \end{bmatrix}\). Remember to flip the filters.

📗 Answer: . Calculate

📗 [2 points] \(C\) is the boolean whether you have COVID-19 or not. \(F\) is the boolean whether you have a fever or not. Let \(\mathbb{P}\left\{F = 1\right\}\) = , \(\mathbb{P}\left\{C = 1\right\}\) = , \(\mathbb{P}\left\{F = 0 | C = 1\right\}\) = . Given that you have COVID-19, what is the probability that you have fever? Note: this question uses random fake data, please refer to CDC for actual data.

📗 Answer: . Calculate

📗 [2 points] A traffic light repeats the following cycle: green seconds, yellow seconds, red seconds. A driver saw at a random moment. What is the probability that one second later the light became ?

📗 Answer: . Calculate

📗 [3 points] Which of the following values of \(\mathbb{P}\left\{B\right\}\) is possible if \(\mathbb{P}\left\{A\right\} = \mathbb{P}\left\{A, B\right\}\) = ?

📗 Choices:

📗 Calculator: . Calculate

📗 [3 points] Given two Boolean random variables, \(A\) and \(B\), where \(\mathbb{P}\left\{A\right\}\) = , \(\mathbb{P}\left\{B\right\}\) = , and \(\mathbb{P}\left\{A| \neg B\right\}\) = , what is \(\mathbb{P}\left\{A|B\right\}\)?

📗 Answer: . Calculate