Arcesium SDE Intern Interview Questions and Answers

Morgan Stanley is a top-tier investment bank with a strong reputation for innovation and excellence.

• Morgan Stanley has a long history of success in the financial industry

• The company is known for its innovative approach to investment banking

• Morgan Stanley has a strong reputation for excellence in research and analysis

• The firm offers a wide range of services to clients, including wealth management and investment banking

• M...read more

Tower and Morgan Stanley are both financial services companies.

• Tower is a global investment management firm with over $1 trillion in assets under management.

• Morgan Stanley is a multinational investment bank and financial services company.

• Both companies offer a range of financial services including wealth management, investment banking, and asset management.

• Tower is known for its focus on sustainable investing, while Mo...read more

The job profile offered is for an analyst position. A PhD is not required for this role.

• The job involves analyzing data and providing insights to clients

• A PhD is not necessary as the role focuses more on practical application of analytical skills

• The job may require a bachelor's or master's degree in a related field

• Examples of job responsibilities may include data collection, statistical analysis, and report writing

Innovations to minimize cost of pen

• Use recycled materials for pen body and ink

• Simplify design to reduce production costs

• Implement refillable ink cartridges to reduce waste and cost

• Partner with companies for bulk purchasing of materials

• Automate production process to reduce labor costs

Prove N>=N^.5+N^(1/3)+N^(1/4) for N>=a

• Use AM-GM inequality

• Substitute N with a and prove the inequality holds

• Use calculus to find the minimum value of the expression

Finding the probability distribution for the minimum of two random variables with given distributions.

• Use the formula P(min(x,y)>z) = P(x>z)P(y>z)

• Integrate over the range of z to get the distribution of min(x,y)

• Final distribution is 2ke^(-kx)ue^(-ux)exp(-uz)

Given prob. p of dying out and prob. (1-p) of spawning into 2, find prob. of dying out starting from 1 organism.

• Use probability tree to visualize outcomes

• Probability of dying out starting from 1 is p + (1-p) * (probability of dying out starting from 2)^2

• Solve recursively to get final answer

Probability of a rectangle being inside a unit circle with p chosen uniformly on the circle and q inside the circle.

• The probability can be found by calculating the ratio of the area of the rectangle to the area of the circle.

• The area of the circle is pi and the area of the rectangle can be found using the distance between p and q.

• The probability is 1/4.

• Example: If the distance between p and q is 0.5, then the area of t...read more

Find local minima of an array in o(log n) in functional programming.

• Use binary search to find the local minima.

• Check if the mid element is a local minima, if not, move towards the lower side.

• If the mid element is greater than its left element, move towards the left side, else move towards the right side.

• Repeat until a local minima is found.

• Example: [5, 3, 2, 4, 6, 8, 9] -> local minima is 2.

Code to sort a list without pipes

• Use a sorting algorithm like bubble sort, insertion sort, or selection sort

• Implement the algorithm in the programming language of your choice

• Test the code with different input sizes and types

To find an even length palindrome in a string in O(n), we can use the two-pointer approach.

• Initialize two pointers at the center of the string.

• Expand the pointers outwards while checking if the characters at both pointers are equal.

• If they are not equal, return the previous substring as the even length palindrome.

• If the pointers reach the end of the string, return the entire string as the even length palindrome.

Possible values of determinant of matrix A given Avi=Vj for n linear vectors

• The possible values of |A| are non-zero as the given vectors are linearly independent

• The value of |A| can be calculated using the formula |A| = (-1)^n * det(A)

• If the given vectors are orthogonal, then |A| is the product of the magnitudes of the vectors

A and B play a game with unfair coin. A wins if # of heads > #tails +1 at any point. Find prob. of A winning.

• The game is played with an unfair coin with P[Heads]=p

• A wins if # of heads > #tails +1 at any point

• Find the probability of A winning

Find two elements in a sorted array that add up to a given sum in linear time.

• Use two pointers, one at the beginning and one at the end of the array.

• If the sum of the two pointers is greater than the target, move the right pointer to the left.

• If the sum of the two pointers is less than the target, move the left pointer to the right.

• Repeat until the sum is found or the pointers meet.

• Example: Given [1, 2, 3, 4, 5] and ta

The probability of element at 20th position landing up at 31st position after the first iteration.

• The probability depends on the size of the dataset and the algorithm used for iteration.

• If the algorithm involves swapping adjacent elements, the probability is higher.

• If the dataset is sorted in a way that the element at 20th position is adjacent to the element at 31st position, the probability is 1.

• The probability can be...read more

Expected number of collisions between randomly moving ants on a rod after 30 seconds.

• Calculate the probability of two ants colliding at any given time.

• Use the formula for expected value to find the expected number of collisions.

• Assume that the ants are point masses and collisions are perfectly elastic.

• Consider the possibility of multiple ants colliding at the same time.

• Simulation can also be used to estimate the expect

Counting permutations where numbers between u and i+1 are less than i for all i in the permutation.

• The first number in the permutation must be 1.

• For each i in the permutation, all numbers between u and i+1 must be less than i.

• Use dynamic programming to count the number of valid permutations.

• The answer is (n-1)th Catalan number.

• Example: for n=4, the answer is 5.

Finding f(n) for a normal standard distribution with a given constant k.

• Calculate the product of probability density function and cumulative distribution function.

• Integrate the product of f(x) and F(kx) from -inf to +inf.

• The value of k is a constant greater than 0.

Number of inversions in an array in O(nlogn) time.

• Use merge sort algorithm to count inversions

• Divide the array into two halves and recursively count inversions

• Merge the two halves and count split inversions

• Time complexity is O(nlogn)

Debugging steps for a slow web portal

• Check server load and resource usage

• Analyze network traffic and latency

• Review code for inefficiencies and optimize

• Use profiling tools to identify bottlenecks

• Consider caching and content delivery networks

• Test and monitor performance after changes

Denormalization, indexing, caching, and partitioning can improve query performance.

• Denormalize the data to reduce the number of joins required for queries.

• Create indexes on frequently queried columns to speed up search.

• Cache frequently accessed data in memory to avoid disk reads.

• Partition large tables into smaller ones to reduce the amount of data that needs to be scanned.

• Use query optimization techniques like query re...read more

Sorting algorithm organizes data in a specific order.

• Choose a sorting algorithm based on the data size and type.

• Common sorting algorithms include bubble sort, insertion sort, and quicksort.

• Implement the chosen algorithm in code.

• Test the algorithm with sample data to ensure it sorts correctly.

My parents inspire me the most.

• Their hard work and dedication to providing for our family motivates me to work hard.

• Their unwavering support and encouragement has helped me overcome challenges.

• Their values and principles have shaped me into the person I am today.

• Seeing their sacrifices and selflessness inspires me to be a better person.

A leader should possess qualities like vision, communication, empathy, integrity, and adaptability.

• Vision: Ability to see the big picture and set goals accordingly

• Communication: Ability to convey ideas clearly and listen actively

• Empathy: Ability to understand and relate to others' emotions and perspectives

• Integrity: Consistency in values, actions, and decisions

• Adaptability: Ability to adjust to changing circumstances a

Morgan Stanley is a top-tier investment bank with a strong reputation for excellence and innovation.

• Morgan Stanley has a long history of success in the financial industry

• The company is known for its innovative approach to investment banking

• Morgan Stanley has a global presence and offers a wide range of services to clients

• The firm has a strong commitment to diversity and inclusion

• Morgan Stanley is a great place to work

DB is a crucial component for storing and managing data in various applications.

• DB stands for Database and is used to store and manage data in various applications.

• It allows for efficient data retrieval and manipulation.

• There are various types of databases such as relational, NoSQL, and graph databases.

• Examples of popular DBMS include MySQL, Oracle, MongoDB, and Neo4j.

Yes, an algorithm I designed at Microsoft can be applied to a problem in the stock market domain.

• I designed an algorithm at Microsoft that can be used in the stock market domain

• The algorithm can be applied to solve a specific problem in the stock market

• The work I did at Microsoft has potential applications in the financial industry

Answering a question about estimating quant score and overall score in finance.

• I estimate my quant score to be X based on my preparation and practice.

• Adding my quant score to the avg finance score may or may not result in the highest overall score, as it depends on the scores of other candidates.

• However, I am confident in my abilities and believe that I can perform well in both areas.

• I am open to discussing my preparat...read more

Tower Research does not align with my career goals and interests.

• I am looking for a company that aligns with my values and interests

• I have researched Tower Research and do not feel it is the right fit for me

• I am seeking a company with a strong focus on innovation and collaboration

• Tower Research may be a great fit for others, but it is not the right fit for me

One of the best projects I worked on was developing a mobile app for a non-profit organization.

• The app was designed to help the organization's volunteers easily track their hours and tasks.

• I worked closely with the non-profit to understand their needs and create a user-friendly interface.

• The app was well-received by the volunteers and helped the organization better manage their resources.

• I also implemented a feature th...read more