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Match the correct method used to determine the distance of different celestial objects. (Note: each different method must be used only once.)

Order chronologically different phases of a binary system formed by a primary star of 5 solar masses and a secondary star of 1.5 solar masses. (Hints: the evolution of stars of different mass occurs on very different timescales).

In observational astronomy, information can be obtained with three different tools: , which describe the spatial distribution of photons, , which illustrate the temporal evolution of the source intensity, and , diagrams of  intensity vs. frequency (or wavelength). In general, in black hole systems, the direct imaging of the (which emits mostly in the visible, UV and soft X-ray bands) is impossible because of its compactness: its subtended angle is too small for the angular resolution of current telescopes. However, one can often resolve the (when present), thanks to interferometric observations in the radio band.

Coding-based: For the given data set in the python file, which of the following is not a predictor variable?

Coding-based: For the given data set in the python file, apply standardization to the predictor variables and report the standard deviation of the predictor variable ‘CHAS’ obtained after standardization.

We are using the AdaBoost algorithm to improve the performance of our classifier. We have initialized 3 base (weak) models to be trained using the training data. After training model 3 (a weak learner) on the training data, model 3 is used to predict classes of 5 samples. Below are the predicted and the actual classes of the 5 samples along with the weights to the samples. Compute the misclassification rate and select the correct answer from the given options.

Coding-based: For the given data set in the python file, do the following: Type this in a cell: random.seed(123) And then split the data into train and test data sets with a test_size=0.10 and random_state=1. Which of the following data sets contain record #32 with the following features? 1.35472 0.0 8.14 0 0.5380 6.072 100.0 4.1750 4 307 21.0 376.73 13.04  

The plot below shows data points between 2 predictor variables (x1 and x2) for a 2-class classification problem (red vs blue): What can be said about the relationship between the predictor variables and the response variable? Select one of the following options:

There are two types of data sets given to you: a) one in which the relationship between the predictor and response variable can be expressed using a parametric form, and b) another in which the relationship between the predictor and response variable cannot be expressed using a parametric form. If you are allowed to only use a tree-based regressor, which of the following data sets would you be able to fit well?

Which of the following statements is false with respect to the Random Forests method? a) It helps in reducing the correlation among various trees. b) It uses samples without replacement to train individual decision trees. c) Given p number of predictors in a problem, it uses k < p predictors at each node/split to select the best predictor. d) It uses m number of trees and aggregates their predictions to determine the response variable value.