Suppose you have three random variables. The correlation between A and B is 0.6, the correlation between A and C is 0.8. What is the range of correlation between B and C?
Quantitativ Interview Questions
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What is the probability of a Brownian motion hit 1 before hitting -2. The Brownian motion starts at 0.
You have a deck of 52 cards, and you keep taking pairs of cards out of the deck. if a pair of cards are both red, then you win that pair; if a pair of cards are both black, then I win that pair; if a pair of cards has one red and one black, then it's discarded. If, after going through the whole deck, you have more pairs than I do, then you win $1, and if I have more pairs than you do, I win $1. What is the value of this game in the long run?
Suppose N students participate in a coin flip experiment, when they get heads they stop, when they get tails they keep going. All students will stop after the second trial no matter the results. Y is the binary indicator of whether they claim they cheated in the experiment. Estimate how many students cheat in this experiment.
Given a round table, randomly place three legs under the table, what is probability that the table will fall?
You have two decks of cards: a 52 card deck (26 black, 26 red) and a 26 card deck (13 black, 13 red). You randomly draw two cards and win if both are the same color. Which deck would you prefer? What if the 26 card deck was randomly drawn from the 52 card deck? Which deck would you prefer then?
a deck of pokers. Three choices: A: 26 black, 26 Red; B: 13 black, 13 Red; C: random 26 card from the deck. Take the first two cards, if same color, the win $1, otherwise lose $1. Which deck is best for you if you are playing? Why? How to do simulations? How to draw the random pile of 26 cards?
A clock on the wall falls and breaks into 3 pieces with the same sum of numbers. What are the three pieces?
Interesting question: From a deck of 52 cards pick 26 at random. From this set of 26 you pick two cards. You win if the both of these cards are of the same color. Is this a game you would prefer over one in which you win by picking two (first two picks) of the same color at random from a deck of 26 with equal number of black and red cards
Suppose that you have a fair coin. You start with $0. You win 1$ each time you get a head and loose $1 each time you get tails. Calculate the probability of getting $2 without getting below $0 at any time.
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