Problem A4 on this year's Putnam exam was an interesting probability problem, so I thought I'd post it here. For those who aren't familiar with the Putnam, it is an extremely hard college math contest, in which the median score is typically 0. Not 0 questions right, 0 partial credit. So this question is vastly harder than what you would ever see on P.
Finding the distribution of X that has the minimum possible value of P[X=0] isn't so bad. The hard part of the problem is proving that that is indeed the minimum. I can post hints and a solution next week if there is interest.
Quote:
Originally Posted by 2014 Putnam A4 Suppose X is a random variable that takes on only nonnegative integer values, with E[X]=1, E[X^2]=2, and E[X^3]=5. (Here E[Y] denotes the expectation of the random variable Y.) Determine the smallest possible value of the probability of the event X=0. |
Finding the distribution of X that has the minimum possible value of P[X=0] isn't so bad. The hard part of the problem is proving that that is indeed the minimum. I can post hints and a solution next week if there is interest.
2014 Putnam A4
