# Rebellion Research Employment Application Form

We are currently accepting applications for computer programming / quant positions at Rebellion Research. If you are interested in applying for one of these positions, please complete the form below. In addition to filling out this form, please also send your resume to jobs@rebellionresearch.com. Note that you may still be offered an interview even if you do not know the answer to all of the questions below. We will contact you via email if we are ready to interview you. Thank you very much for taking the time to apply, we look forward to hearing from you!
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## Programming [2/6]

Consider the function below written in an unknown language. The questions below will refer to this function. Assume that this programming language has the following characteristics: 1. It uses zero based indexing of arrays (so 0 is the location of an array's first item). 2. The function size() is used to get the number of elements in an array 3. Code crashes if you access an element of an array that doesn't exist 4. The keyword "function" defines a new function, 5. In functions, it passes arrays by reference, not value. 6. Variable types do not need to be explicitly specified, but the variable ara is an array. 1 function cyk(ara): 2 i = 0 3 s = ara[0] 4 while i < size(ara): 5 ara[i] = ara[i+1] 6 i = i + 1 7 if size(ara) > 1: ara[size(ara)-1] = s 8 return ara

## Linear Algebra [4/6]

While knowledge of linear algebra is a plus, it is not necessary. If you don't know any linear algebra, just leave these questions unanswered.

 True False Not Sure M must be invertible (i.e. there exists a matrix W such that W M is the identity matrix) M M' = M' M (where M' is the transpose of M) If x is a real valued vector, and M x = 0, then that necessarily implies that x = 0

## Risk [5/6]

Consider a purely probabilistic game that you have the opportunity to play. Each time you play there are n potential outcomes x1, x2, ..., xn (each of which is a specified gain or loss of dollars) These outcomes x1, x2, ..., xn occur with the probabilities p1, p2, ..., pn respectively (where p1 + p2 + ... + pn = 1.0 and 0 <= pi <= 1 for each i). Positive xi values mean a gain of |xi| dollars and negative values mean a loss of |xi| dollars. Assume that x1, x2, ..., xn and p1, p2, ..., pn are all known quantities. Furthermore, assume that each play of the game takes up one hour of your time, and that only you can play the game (you can't hire someone to play for you). Let E be the game's expected value. That is, E = p1 x1 + p2 x2 + ... + pn xn. Let S be the game's standard deviation. That is, S = SquareRoot( p1 * (x1 - E)^2 + p2 * (x2 - E)^2 + ... + pn * (xn - E)^2 ).

## Education [6/6]

Please note that we have offered internship positions to candidates of all different education levels, from high school through PhD.

## Other/Optional

Thank you for taking the time to complete the application process! After you submit this form, make sure to send your resume to us at jobs@rebellionresearch.com.