Here’s a secret about quant and finance interview questions: They don’t often relate to finance. In trading interviews, probability questions are asked in the form of quantitative problems, and candidates are asked to make calculations based on the information given.
To do well in these interviews, you need intermediate-to-advanced knowledge of statistics, probability, econometrics, and, increasingly, computer science. Although finance-specific knowledge is helpful, you don’t need it to pass the interview.
Expected value is a fundamental concept in statistics and probability theory that plays a crucial role in various fields, including finance, trading, data science, and decision-making under uncertainty. Understanding expected value is essential for anyone aspiring to succeed in these fields.
This article provides a comprehensive guide to expected value interview questions, covering various aspects of this concept and its applications. By studying these questions and their answers, you can gain a deeper understanding of expected value and prepare for your next interview with confidence.
What is Expected Value?
Expected value, also known as the mean or average, is a measure of the central tendency of a probability distribution. It represents the average outcome of an experiment or event over many repetitions, considering all possible outcomes and their respective probabilities.
Why is Expected Value Important?
Expected value is a powerful tool for making informed decisions under uncertainty. By calculating the expected value of different options, we can estimate the average outcome and choose the option with the highest expected value. This approach helps us maximize our chances of achieving a favorable outcome, even when the future is uncertain.
Expected Value Interview Questions
Here are some common expected value interview questions that you may encounter
1. What is the expected value of rolling a fair six-sided die?
Answer: The expected value of rolling a fair six-sided die is 3. 5. To find this, add up the values of all the outcomes (1, 2, 3, 4, 5, and 6) and divide by the number of outcomes.
2. How would you calculate the expected value of a discrete random variable?
Answer: To calculate the expected value of a discrete random variable, multiply each possible outcome by its probability and then sum these products.
3. What does the expected value have to do with the Law of Large Numbers?
Answer The Law of Large Numbers states that as the number of trials or observations increases, the actual result will converge to the expected result The expected value provides a ‘center’ or ‘mean’ towards which these results gravitate
4. How would you explain the link between the Central Limit Theorem and Expected Value?
Answer The Central Limit Theorem states that if you take a large number of independent and identically distributed random variables, their sum (or average) will be approximately normally distributed, regardless of the original distribution shape This normal distribution will have a mean equal to the EV of the individual distributions
5 How would you use Expected Value in risk assessment and management in a real-world setting?
Answer Expected Value (EV) is a statistical tool used in risk assessment and management to quantify the average outcome of an event when the future holds uncertainty. It’s calculated by multiplying each possible outcome by its probability then summing these.
6. If given a probability distribution, how would you compute the Expected Value without using any statistical software?
Answer: To compute the Expected Value (EV) from a probability distribution manually, you need to multiply each possible outcome by its corresponding probability and sum these products. The formula for EV is ∑[x * P(x)], where x represents each possible outcome and P(x) is the probability of that outcome occurring.
7. Can you describe a scenario where the expected value would be misleading, and how you would address it?
Answer: A misleading scenario for expected value could be in a lottery. The expected value is calculated by multiplying each possible outcome by its probability and summing these products. For instance, if a lottery ticket costs $1 with a 1 in 100 million chance of winning $50 million, the expected value would be $0.50 ($50M * 1/100M). This suggests that buying a ticket is a good investment.
8. How would you interpret a negative expected value result in a business scenario?
Answer: A negative expected value in a business scenario signifies potential loss. It’s an indicator that the average outcome of a decision, when considering all possible outcomes and their probabilities, is less than zero. This could be due to high costs, low revenues, or both.
9. In what ways can the concept of Expected Value be relevant in machine learning algorithms?
Answer: Expected Value (EV) is a fundamental concept in machine learning algorithms. It’s used to predict outcomes based on probability distributions, which are often inherent in data sets used for training these algorithms.
10. Describe how Expected Value can be applied in an optimization problem.
Answer: Expected Value (EV) is a statistical concept used in optimization problems to predict the average outcome over numerous trials. It’s calculated by multiplying each possible outcome by its probability and summing these products.
11. How would you estimate the expected value of a continuous random variable?
Answer: To estimate the expected value of a continuous random variable, we use integration instead of summation. The expected value (E[X]) is calculated by integrating over all possible values that X can take on, each multiplied by its probability density function (pdf).
12. Can you write an SQL query to compute the expected value given a dataset with probabilities and outcomes?
Answer: Yes, to compute the expected value using SQL, we can use a simple SELECT statement with SUM function. Assuming we have a table named ‘dataset’ with columns ‘probability’ and ‘outcome’, the query would look like this:
SELECT SUM(probability * outcome) AS Expected_Value FROM dataset;13. How would you handle a situation where the expected value of a decision is the same, but the risk associated with the decisions are different?
Answer: In a situation where the expected value of two decisions is identical, but the risks associated are different, I would employ risk analysis techniques to make an informed decision.
14. How can Expected Value be used in hypothesis testing? Provide an example.
Answer: Expected Value (EV) is a statistical tool used in hypothesis testing to predict the average outcome of an experiment over many trials. It’s calculated by multiplying each possible outcome by its probability and summing these products.
15. Describe the relationship between Expected Value and Variance.
Answer: Expected value and variance are two fundamental concepts in statistics, both providing different insights about the probability distribution of a random variable. Expected value is essentially the mean of a random variable’s possible outcomes weighted by their respective probabilities. It gives us an idea of what to expect on average from numerous trials.
By thoroughly studying these expected value interview questions and their answers, you can gain a deeper understanding of this crucial concept and prepare for your next interview with confidence. Remember to practice explaining your answers clearly and concisely, demonstrating your knowledge and problem-solving skills.
[ Write a function that takes input as the number of tosses and a probability of heads]
Write a function that takes in the number of flips and the chance that each one will land on its head and returns a list of results that are chosen at random and are the same length as the number of flips. Each result represents the outcome of a coin toss, where ‘H’ represents heads and ’T’ represents tails.
(https://www.interviewquery.com/questions/simulating-coin-tosses)
How Are Stats & Probability Questions Framed?
Quant interview questions typically take the form of brainteasers or probability case studies. You’re provided with a scenario and make a calculation based on the provided information. The most common probability interview question types in quant finance interviews are:
- Conceptual probability questions are more difficult because they are based on definitions and usually come before more difficult case studies.
- Probability case studies: In these questions, you are given a situation and asked to figure out how likely it is that something will happen. These questions often relate to dice rolls or card draws.
- Distribution case questions ask you to think about the different outcomes that could happen in certain situations based on distributions.
- A statistical analysis question might give you data and ask you to make a statistical prediction based on it.
