You have 10 mice and 1000 bottles of wine. You also have 24 hours before a party, and one of the bottles has been tainted with a slow acting poison, which takes 24 hours to kill a mouse. In the 24 hours you have remaining, how many bottles can you guarantee safe for human consumption (assume humans and mice react identically)? Assume the lethal dosage is insignificant relative to the size of the bottle.
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?
Assume X_i ~ i.i.d. Unif(0,1). What is the expected length of a sequence that is monotonically increasing when drawn from the distribution?
Expected number of flipping coins of getting two consecutive faces.
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?
You flip four coins. At least two are tails. What is the probability that exactly three are tails? Do this in your head, you are not allowed to write anything down for this question.
a, b, c are integers. Such that a^2 + 2bc = 1; b^2 + 2ac=2012, find all the possibles values of c^2 + 2ab.
What is the probability of breaking a stick into 3 pieces and forming a triangle?
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 is the probability of a Brownian motion hit 1 before hitting -2. The Brownian motion starts at 0.
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