Recent content by holemole

Well I thought the ball example and the card example are separate cases, since the card example shows subsequent draw as just one case whereas the ball example explicitly limits the cases in question to those with second ball as yellow. The more I think about it I think those two questions...

This is different from the original question because this process, regarding our net profits, would leave out the cases where first is diamond but next three are of different suit. It would only process our earning only with cases where three diamonds are present. Three consecutive diamonds...

10/49 is the probability of the FIRST draw to be a diamond when three draws after the first are all diamonds.

first single card draw is consisted of equally probable events, isn't it? This is completely true, but we're not trying to find number of events concerning first draw as diamond amongst total number of events where 3 consecutive draws after single draw are diamonds. 3 diamonds is not our...

Could you explain to me why this is the case?

i understand that information has changed. Nevertheless I'm not convinced that the information affects the original draw, since the population of the first draw doesn't necessarily change before I somehow pick 13 diamonds from 51 cards, which I didn't. I'm aware that if any new information that...

Setting is like this: I have 52cards of 4 shapes. that's 13 each. I take one card out and put it in a hat. now with 51card I draw 3 consecutive cards. It happens to be that I picked 3 diamonds. Now I want to find the probability of the card in the hat be a diamond. My friend said it...

Kind of figured it out by myself now. Reason why the proof states E is because while E is quadratic form of A, Q is again quadratic form of E. Thus sign definiteness of Q can rely on det(E), which is attainable if we follow the proof's manipulation ofchanging the basis of the bordered hessian...

http://www.math.northwestern.edu/~clark/285/2006-07/handouts/lin-constraint.pdf It's actually proof of finding sign definiteness of quadratic form with linear constraints with sign of submatrices of bordered hessian. The proof is from page 2~page 3. I have 2 questions: 1. From about...