The average height and weight of a group of people is 175cm and 70kg; Find the upper bound of the portion of the people who are over 200cm and over 100kg.
I thought about Markov inequality, but I think height and weight are related? So P(H>200, W?100) can not be decomposed as P(H>200)P(W>100).
Get stuck. Anyone has any idea? Thanks!.
EDIT: This problem asks for a upper bound, so a reasonable tight upper bound is expected I suppose.
Given the problem as stated, I think the only way to bound it is as follows: The most that can be over $200$ cm tall is $\frac 78$, which assumes those people are exactly $200$ cm and the rest are $0$ cm tall. The most that can be over $100$ kg is $\frac 7{10}$, which assumes everybody is either $100$ kg or $0$ kg. The upper bound on the number of people who are both is the lower of these-$\frac 7{10}$ That leaves us $\frac 7{40}$ who are $0$ cm and $100$ kg?!?!.