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Quantitative trading interviews usually include a series of brain teasers, mental arithmetic questions, and statistics questions. These questions vary from company to company, but typically come up in multiple rounds of interviews, with the first round usually being an online test. These issues are especially common in entry-level positions and internships.
For mental arithmetic problems, the best way to prepare is to practice over and over again within a time limit. Usually these questions come in the form of an online test and you need to answer as many as you can in a few minutes. For example, Optiver gives you 8 minutes to complete 80 mental arithmetic problems, covering integers, decimals, and fractions. If you want to stand out from the competition, it is recommended to score at least 55 points.
As for the statistics part, it is recommended that you review the statistics textbooks you learned in college. Sheldon Ross's ["Preliminary Probability Theory"] (https://a.co/d/6H9L2xX) is a good choice. The book explains the mathematical principles of probability theory in detail and provides a large number of exercises for you to practice. In addition to the resources mentioned above, the best way to make breakthroughs in brain teasers and statistics problems is to practice more variations of the problems. In this article, we will provide you with some practice questions that may appear in your next quantitative trading interview. Scroll to the bottom of the page to find detailed answers and explanations.
Let's say you're taking the SAT math section and your scores range from 200 to 800. Scores for this part of the exam are normally distributed, with a mean of approximately 500. When the test scores are released, your friends tell you that your score is more than 1 standard deviation above the mean. Based on this information, what is the probability that your score is more than 2 standard deviations above the mean?
a) 16%
b) 9%
c) 50%
d) 27%
The average score of the 6 exams is 81 points. After adding the seventh test scores, the mean becomes 83 points. What is the score of the seventh test?
a) 88
b) 97
c) 92
d) 95
A fair coin is tossed 6 times. What is the probability of getting exactly 4 heads?
a) 5/32
b) 15/64
c) 13/64
d) 5/16
What is the next number in each sequence?
Part A: 2, 4, 7, 11, 16, _
a) 21
b) 22
c) 23
d) 24
Part B: 81, -54, 36, -24, _
a) -12
b) 12
c) 16
d) 18
You're planning a four-day getaway but are worried about the weather. At the resort, 80% of the days are sunny and every day is independent. For you to have a good time, it needs to be sunny for at least three out of four days. What is the probability that you have fun?
a) 64/125
b) 128/625
c) 256/625
d) 512/625
**The correct answer to this question is option a (16%). ** According to the normal distribution model, 68% of the data will fall within one standard deviation of the mean. That is, the probability that a data point deviates from one standard deviation is 0.32 (1 - 0.68). At the same time, 95% of the data will fall within two standard deviations of the mean, so the probability of a data point deviating from two standard deviations is 0.05. 0.05 / 0.32 ≈ 0.16.
**The correct answer to this question is option d (95). **
It is mentioned in the question that the average score of 6 tests is 81. Expressed mathematically as X / 6 = 81, where X is the sum of the previous six test scores. By calculation, we get X = 486. Next, we need to find the scores for the seventh test. The same formula is expressed as (486 + Y) / 7 = 83, where Y is the score of the seventh test. By calculation, we get Y = 95.
**The correct answer to this question is option b (15/64). **
First, we count all the possible outcomes of tossing a coin six times. Since there are two outcomes for each coin toss, the total number of possibilities is 2^6 = 64. To calculate the number of times we get four heads, we can use the combining formula n!/(r!(n-r)!). The total number of times is 6, and 4 times are chosen as heads, so we get 6!/(4!*2!) = 15. So, the answer is 15/64.
**The correct answer for Part A is option b (22) and the correct answer for Part B is option c (16). **
For part A, we observe an increase in the magnitude between each consecutive number (an increase of 2 from 2 to 4, an increase of 3 from 4 to 7, and an increase of 4 from 7 to 11). Expressed mathematically as n(n+1)/2 + 1. For part B, assume we reverse the sequence. Doing so, we find that each successive number is (current number + half the current number) multiplied by -1. For example, (-24 + half -24) times -1 equals 36. Therefore, the answer to this question is a number that, when added to half of it and multiplied by -1, gives -24. So, the answer is 16.
**The correct answer to this question is option d (512/625). **
Since the question asks us to calculate the probability that at least 3 of 4 days will be sunny, we can separately calculate the probability of exactly 3 days being sunny and exactly 4 days being sunny, and then add them together. The probability that exactly 3 days will be sunny is the number of combinations of 3 days selected from 4 days, multiplied by the probability of sunny days raised to the power of 0.8, and then multiplied by the probability of rainy days of 0.2. Expressed as:
(4C3) * (0.8^3) * (0.2^1) = 0.4096, where (4C3) is the combination formula, n=4, r=3.
Similarly, the probability that all 4 days are sunny is calculated as:
(4C4) * (0.8^4) * (0.2^0) = 0.4096
Adding these two probabilities gives us 0.8192, which is option d.
Thank you for reading this article. Hopefully these interview questions will help you prepare for your interview for a quantitative trading position.
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