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Laura C.
Physics PhD from University of Michigan with ample tutoring experience
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Calculus
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Question:

What is the derivative of f(g(x)) with respect to x?

Laura C.

The chain rule dictates that $\frac{df}{dx} = \frac{df}{dg} \frac{dg}{dx}$.

Physics
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Question:

What force is the action-reaction pair of your weight on Earth? What is its magnitude? Its direction?

Laura C.

This question pertains to Newton's 3rd Law. A person's weight on Earth is equal to $W = m g$ where $m$ is the person's mass and $g = \frac{G M_E}{R_E^2}$, where G is Newton's gravitational constant, $M_E$ is the mass of the Earth, and $R_E$ is the radius of the Earth. A person's weight on Earth, $W = m g$ is the force that the Earth exerts on the person; this force is directed from the person's center of gravity towards the Earth's center of gravity. The action reaction pair of a person's weight on Earth is, then, the force the person exerts on the Earth, equal in magnitude to $W$, but directed in the opposite direction -- that is, pointing from the center of gravity of the Earth towards the center of gravity of the person.

Data Science
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Question:

How can you discern feature importance when performing a machine learning classification task using random forests?

Laura C.

To prevent overfitting of the model by the random forest classification algorithm, add several random noise features to your data. When assessing feature importance (which can be done using sklearn), those features whose feature importance exceeds that achieved by the random noise variables are the relevant, predictive features you should keep in subsequent iterations of your model.

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