If X, Y and Z are three random variables such that X and Y have a correlation of 0.9, and Y and Z have correlation of 0.8, what are the minimum and maximum correlation that X and Z can have?
Research Intern Interview Questions
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Suppose you have two covariance matrices A and B. Is AB also a covariance matrix? Suppose that, by plain dumb luck, we also have that AB=BA. Is AB a covariance matrix under this additional condition?
Drawing a pair of (x, y) from a joint Gaussian distribution with 0 covariance. Knowing the stndard deviations of x and y and knowing z = x + y, what is your best guess for x?
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?
What are index funds and how are they traded in markets?
Suppose you have 100 GB of data that you want to sort, but you only have 1 GB of memory. How would you sort this data?
A clock on the wall falls and breaks into 3 pieces with the same sum of numbers. What are the three pieces?
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?
1, 2, 3 from exp, ln, sqr, sqrt, sin, cos, tg, arcsin, arccos, arctg and 0
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