Hey all. I'm working on a problem that is stated as follows:
Ann cuts an ordinary deck of 52 cards and displays the exposed card.Andy cuts the remaining stack of cards and displays his exposed card. Counting jack,queen, and king as 11, 12, and 13, let X and Y be the numbers on the cards that Ann andAndy expose, respectively. Find Cov(X, Y ) and interpret the result.
In this example are X and Y independent? They're saying that Ann cuts the deck, and from the cut deck Andy picks his card. So I interpret they each have an equal probability of picking any (value) card. If Ann gets a ace of spades, Andy can still get the ace of hearts, diamonds, or club with (just about) equal probability. However their answer shows that there is a strong negative correlation. They argue this makes sense intuitively, but I don't really see it.
Can any offer some help?
Ann cuts an ordinary deck of 52 cards and displays the exposed card.Andy cuts the remaining stack of cards and displays his exposed card. Counting jack,queen, and king as 11, 12, and 13, let X and Y be the numbers on the cards that Ann andAndy expose, respectively. Find Cov(X, Y ) and interpret the result.
In this example are X and Y independent? They're saying that Ann cuts the deck, and from the cut deck Andy picks his card. So I interpret they each have an equal probability of picking any (value) card. If Ann gets a ace of spades, Andy can still get the ace of hearts, diamonds, or club with (just about) equal probability. However their answer shows that there is a strong negative correlation. They argue this makes sense intuitively, but I don't really see it.
Can any offer some help?