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Tutor profile: Anita S.

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Anita S.
Tutor for three years, Graduate Student in Biomedical Engineering
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Questions

Subject: Python Programming

TutorMe
Question:

What will the following code output? x1 = [1, 4, 3] if x1[1] > 2: x2 = [7 + s for s in x1] else: x2 = [2*s for s in x1] print(x2)

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Anita S.
Answer:

This code uses control statements (if/else) to decide which lines should be run. If the 1-th element of x1 is greater than 2, the first statement is run, if it is not then the computer will run the second statement. Python always starts at an index of 0, so the 1-th element in the list is actually the second element: x1[1] = 4. Therefore, it will enter the "if" case. The code then asks Python to perform a list comprehension -- some convenient syntax that Python has for creating a new list that contains something for every element in some other list. In this case, make a new list in which each element is 7 plus the corresponding element in x1. Therefore Python will print out "[8, 11, 10]".

Subject: Calculus

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Question:

What is the derivative of $$f(x) = \ln(2x-3)$$ ?

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Anita S.
Answer:

Since this question involves a function inside a function, we need to use the Chain Rule. This rule tells us how the rate of change of $$f(x)$$ depends cumulatively on the rate of change of each of its nested parts. In class, you may have learned a proof for why $$\frac{d}{dA}ln(A) = \frac{1}{A}$$. In this case, $$A = 2x- 3$$. That's it for the outer part! Now, for the derivative of $$2x-3$$, we can take the derivative of each term separately: $$\frac{d}{dx} (2x-3) = \frac{d}{dx} 2x- \frac{d}{dx} 3 = 2 $$. Multiplying together (because of the chain rule) we get our final answer: $$\frac{d}{dx} \ln(2x-3) = \frac{1}{2x-3}*2$$ .

Subject: Statistics

TutorMe
Question:

A team of scientists decided to measure the wingspans of fifty seagulls. They found that the mean wingspan was 2 feet, with a standard deviation of one inch. How likely is it that if you see a seagull (from the same population), it will have a wingspan of 2 feet 2 inches or longer? (Assume seagull wingspans follow a normal distribution.)

Inactive
Anita S.
Answer:

We need to find out what proportion of seagulls have a wingspan greater than or equal to 2ft 2 inches. First, we convert from this specific problem to a general z score by subtracting the mean and dividing by the standard deviation, to find out how many standard deviations our point of interest is from the mean. Doing this, we find out that a wingspan of 2 feet 2 inches is 2 standard deviations above the mean (it's unusually long!). To find the probability we are looking for, we just need to get the area under the standard normal curve, to the right of 2 SD above the mean. You can look this up in a z table or using certain software, and you should get about 0.023 (remember to subtract from 1 if the table only gives left-side areas!).

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