Technical Exam: 20 questions on probability, statistics, regression, linear algebra, calculus and a few brain teasers. For example: - A robot sits in the upper left hand corner square of an 5x5 grid. The robot can only move in two directions: right and down and cannot go through the blacked out square. How many possible paths are there for the robot to get to the bottom right hand corner square? - What is the variance of a uniform random variable X with probability density function f(x) = 1 for 1 ≤ x ≤ 2? - Which integer is CLOSEST to the trace of e^A where A is the 2×2 matrix [1/2 0; 0 1/3]. - You and a friend are playing a game that uses fair coins. Suppose that you have 51 coins, while your friend only has 50. You both flip all of your coins and count the number of heads. What is the probability that you flip strictly more heads than your friend does? Data exam: I got 6 csv files and 2 hours to answer questions about the files. You can choose your own programs to work with. I used SQL & Python. There were in total 15 questions, some of which multiple choice. The assignment was about covid restrictions and the impact of the restrictions on stock returns. Csv files were for example a companies.csv, a restrictions.csv (with different restrictions at different companies), a vaccines.csv, a csv file with stock returns, a file with market capitalisation data. Questions were: - what % of companies were in industry X? - Which term describes the market capitalisation? Unimodal / Bimodal / uniform / balanced / positively skewed / negatively skewed / leptokurtic / log normal / etc. - What is the tickr of the French company with the lowest standard deviation of returns? - Calculate the annualised weighted return while a stay-at-home order is in place (including the start and end dates of the stay-at-home order). What is the result for Germany? - 2 questions about OLS regression, to estimate the effect of stay-at-home orders on returns. Codility exam: 3 questions in 1 hour. One of the questions was: You are given an array S made of N strings and an integer K. Choose at most K letters from the alphabet that will allow you to build as many strings from array S as possible. Any of the chosen letters can be used multiple times when building the strings. What is the maximum number of strings that can be built?