Probability and Statistics Concepts

Flashcards covering key concepts in probability, statistics, and finance, along with practical problem-solving techniques.

Expected Number of Flips

The average number of coin flips needed to get 2 heads when flipping a fair coin is 6.

Probability of Sum Less Than 1

In a uniform distribution of two independent numbers drawn from [0,1], the probability that their sum is less than 1 is 1/2.

Expected Rolls to Get a 6

The expected number of rolls of a fair six-sided die to get the first 6 is 6.

Variance of Geometric Distribution

For a geometric distribution with success probability p=1/6, the variance of the number of rolls until the first 6 is 30.

Expected Value of Maximum

The expected value of the maximum of two independent U(0,1) variables is 2/3.

Probability of Sum of Dice

The probability that the sum of two rolled six-sided dice equals 8 is 5/36.

Probability of Disease Given Positive Test

Given a test with 99% sensitivity and specificity, and disease prevalence of 1%, the probability someone who tests positive actually has the disease is about 50%.

Probability that X > Y

For two independent exponential random variables, the probability that X is greater than Y is 1/2.

Expected Number of Fixed Points

In a random permutation of n elements, the expected number of fixed points is 1.

Expected Flips to See HT Pattern

The expected number of flips needed to see the pattern HT (heads then tails) is 4.

Probability at Least Two Share a Birthday

In a group of 30 people, the probability that at least two share a birthday is about 70.6%.

Probability of Standard Normal

For a standard normal variable X, the probability that |X| is greater than 1.96 is about 5%.

Mean and Variance of Bernoulli

For a Bernoulli random variable with parameter p, the mean is p and the variance is p(1-p).

Distribution of Sample Mean

The distribution of the average of 100 independent N(0,1) variables is approximately N(0, 0.1).

Ways to Choose 3 from 10

The number of ways to choose 3 people from a group of 10 is 120.

Arrangements of 'STATISTICS'

The number of distinct arrangements of the letters in 'STATISTICS' is 50,400.

5-Digit Numbers without Repetition

The number of 5-digit numbers formed from digits 0-9 without repetition that do not start with 0 is 27,216.

Subsets of n Elements

A set of n elements has 2^n subsets.

Ways to Place Indistinguishable Balls

The number of ways to place 4 indistinguishable balls into 3 distinct boxes is 15.

Minimum Weighings to Find Heavier Ball

The minimum number of weighings needed to guarantee finding a heavier ball among 8 is 2.

Trailing Zeros in 100!

The number of trailing zeros in 100! is 24.

Identifying Switches and Bulbs

To determine which switch controls which bulb, turn one switch on, then off, then turn another on and check the bulbs for heat.

Measure 45 Minutes with Ropes

To measure 45 minutes with two ropes, burn one from both ends and another from one end, using the first to time a total of 45 minutes.

Monty Hall Problem

In the Monty Hall problem, switching doors after one is revealed to have a goat increases the probability of winning to 2/3.

Probability of Exactly 5 Heads

The probability of getting exactly 5 heads in 10 tosses of a fair coin is approximately 0.246.

Closer to Center in Unit Square

The probability that a randomly chosen point in a unit square lies closer to the center than to any edge is π/16.

Quick Mental Multiplication

17 multiplied by 19 equals 323 by using the formula (a−1)(a+1)=a²−1.

Quick Multiplication of 999x1001

999 times 1001 equals 999,999 using the formula (a−1)(a+1)=a²−1.

Approximate Square Root of 200

The approximate square root of 200 is about 14.14.

Percentage Calculations

13% of 7,400 equals 962.

Approximate 2.3% of 7,400

2.3% of 7,400 is approximately 170.

Quick Mental Computation of 72x28

72 times 28 equals 2,016 by considering it as 72 times (30-2).

Quick Mental Calculation of 88x12

88 times 12 equals 1,056.

Approximate 1/37 as Decimal

1/37 is about 0.027 as a decimal.

Doubling Time with Interest

At 5% interest, it takes about 14 years to double your money using the Rule of 72.

Quick Mental Calculation of 7x49

7 times 49 equals 343 as it can be expressed as 7 cubed.

What is an ETF?

An ETF (Exchange-Traded Fund) is a fund that trades on an exchange like a stock and tracks an underlying basket or index.

Calculating ETF NAV

The Net Asset Value (NAV) of an ETF is calculated as the total market value of underlying assets minus liabilities divided by shares outstanding.

ETF Creation/Redemption

Creation and redemption of ETF shares involves Authorized Participants swapping baskets of securities and ETF shares.

ETF Trading at Premium to NAV

When an ETF trades at a premium to NAV, its market price is above the NAV.

Liquidity of ETFs

An ETF can be highly liquid due to the underlying assets and Authorized Participant activity, regardless of its trading volume.

Tracking Error

Tracking error is the deviation between ETF returns and benchmark index returns.

Stale NAV in International ETFs

An international equity ETF may show a stale NAV during trading if underlying markets are closed.

Market Maker Profit from ETF Mispricing

A market maker can profit when an ETF is above fair value by shorting the ETF and buying the underlying basket.

Bid-Ask Spread

The bid-ask spread is the difference between the best bid and best ask prices, compensating liquidity providers for risk.

Effect of High Volatility on Spread

Bid-ask spreads tend to widen during high volatility due to increased uncertainty and adverse selection risk.

Price Impact of Trades

Price impact refers to the change in market price caused by executing a significant trade.

Market Order vs Limit Order

A market order is executed immediately, while a limit order is executed at a specified price or better.

Adverse Selection in Market Making

Adverse selection is the risk of trading against informed individuals with better information.

Importance of Latency in Trading

Lower latency in trading allows for quicker quote updates, reducing the risk of stale prices.

Order Book Imbalance

Order book imbalance is the difference between buy and sell volume, which can indicate market pressure.

Why Work at Virtu Financial?

Connect your quantitative skills and love of markets to Virtu's tech-driven, team-based culture.

Solving Technical Problems

Use STAR method to explain a challenging technical problem you solved.

Learning from Mistakes

Choose a safe mistake to discuss and highlight what you learned from it.

Handling Pressure and Urgency

Explain how you prioritize tasks and keep a data-driven approach in time-critical situations.

Explaining Complex Topics Simply

Use analogies and avoid jargon to explain complex technical subjects to non-technical audiences.

Making Decisions with Incomplete Data

Show comfort with uncertainty and structured reasoning in scenarios with limited information.

Motivation in Work Environment

State what motivates you, linking it to Virtu's environment emphasizing collaboration and improvement.

Response to Challenging Ideas

Discuss how you calmly assess challenges to your ideas and allow evidence to guide decisions.

Strengths Relevant to Role

Select and discuss strengths that align with the role and provide concrete examples.

Future Career Goals

Express aspirations to advance in a quant/markets role while taking on more responsibilities.