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Tutor profile: Mitchell W.

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Mitchell W.
Data Scientist at Microsoft with 4 years of teaching experience
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Questions

Subject: Python Programming

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Question:

What is the difference between a function and a method in Python?

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Mitchell W.
Answer:

This is a great question since it addresses the object-oriented nature of this programming language. There are 3 main differences: 1) Methods are associated with a class; they are applied to objects of the class for which they are defined. For the most part functions can be applied to any object of the correct type. 2) Methods are called using dot notation, whereas functions are simply called by name. For example, list.append() where append is a method of list objects and print("string") where print is the function with the argument "string". 3) Methods are automatically passed the special parameter "self" as the first argument. In this way, the method can access the variables stored within the object.

Subject: Data Science

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Question:

Can you explain the bias versus variance trade off?

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Mitchell W.
Answer:

To explain the trade off we must first define what each of these terms mean. Variance is the quality of a model to mold to the training data that is fed to it. Therefore, for a model with high variance, you would expect very different models to be produced from different training data. A model with high variance is likely to over fit the data. Bias is the quality of a model to tend towards a set of results regardless of the training data that is fed. For different training sets, you can expect similar models to be output. A model with high bias is likely to under fit data. The trade off occurs because, these two terms are somewhat opposites of each other. Ideally, we would want a model with low variance and low bias. In other words, we want our model to be able to fit data well in order to predict new data points that are presented (low bias), but we do not want a fit that is so aggressive that the model only knows how to properly interpret the training data (low variance). Usually as we tune the model, we need to make sacrifices related to this trade off. For example, if we would like to reduce over fitting, we should decrease variance, but bias will increase and unique data points, that are not noise, in the training set will fail to be predicted. And vice versa. This is the crux of the bias versus variance trade off, you cannot have it both ways.

Subject: Physics

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Question:

If someone throws a ball straight up into the air with a velocity of 4 m/s in the positive direction, what is the velocity when it falls back down and reaches the point at which the ball was thrown? Assume no frictional effects from the air.

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Mitchell W.
Answer:

This question combines two key concepts: vector conventions and conservation of energy. First, since velocity is a vector it has a speed and a direction. The question states that the ball is thrown up in the positive direction, so we can say that in this system, down is considered negative by this convention. Second, what is the speed? This is where conservation of energy comes into play. First we need to define the system. We will consider the point where the ball is thrown to be at a height of zero. Therefore, at the point that the ball is thrown, it has no gravitational potential energy according to the following equation, $$E_g = mgΔh$$. This is because there is not change in height. All the system's energy is kinetic energy. As the ball travels up, the kinetic energy is converted into gravitational potential energy until the ball stops moving at the top of the motion. At this point at the top of the motion all the kinetic energy is converted to gravitational potential energy. Now, when the ball falls back down and reaches the same height at which it was thrown, all the gravitational energy has transferred back into kinetic energy because the difference in height is again 0. According to the equation for kinetic energy, $$E_k= \frac{1}{2} mv^2$$, and since the mass of the object has not changed, the velocity must be the same magnitude as when the ball was thrown. Even though the sign is negative, as discussed earlier, the $$v^2$$ ensures the kinetic energy is the same, which proves it is conserved. Therefore, at the point of return the velocity of the ball is -4 m/s. As a side note, the fact that air friction was neglected is important because we know that none of the energy in the system was converted to heat energy. However, we know that this is not realistic in real life since there are frictional effects and the velocity on the way down will likely have a lower magnitude.

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