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Correlation

(1) Three random variables: X, Y, and Z. If the correlation between X and Y is 0.5, the correlation between Y and Z is 0.6. What is the range of ...


Spanning trees of a two-dimensional n-by-n grid graph

Given a graph G constructed from a two-dimensional n-by-n grid, what is the number of spanning trees of G?


The number of cars in the train

A train is equally likely to have any number of cars from 1 to 100. You are put in one car at random, and it is car 5. In that ...


Wine and Water

There are two glasses of the same size and shape, one containing water and the other containing wine. A man takes a spoon and transfers a spoonful of water from ...


Binary matrices with boundary filled by 1

Given a binary matrix A, i.e. each entry is either 1 or 0, design an algorithm to find a complete set
{A1, A2, ..., Ak} of sub-matrices of A ...