Go to a bar, throw darts for 500 times, 1/2 probability hitting the target, 1 point awarded for each hit. Now getting drunk and throw for 500 times, 1/2 probability hitting the target but 3 points award now. (1) What is the expected score/number of hits? (2) If we got 1100 points, give a feasible (say 15 points) interval estimate of points? (3) How to make this calculations exact?
Approximate the number of book titles ever published
I am thinking of a number that does not contain the digit 1. The product of the digits is 96. What is the smallest possible number in my mind? How about the largest?
derive the formula for the variance of OLS from scratch
suppose you have 500 search algorithm, how to compare them?
Find the minimum of x^x
What is e^{i\pi}
What is the number of ways to reach n-th step of a stair if one can jump up either 1 step or 2 steps?
If W is standard Brownian Motion, for what values of n is W^n still a martingale?
In a set of cereals, there are 4 kinds of coupons. A child wants to collect all the 4 kinds of coupons. How many boxes in average should he buy?
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