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The Art of Problem Solving

This is a community for mathematicians and other rigorous solvers. Feel free to discuss anything about mathematics in this forum. Please repect the general theme of the forum.
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more conditional expectation

Nov 22, 2009
A point X is chosen randomly from the interval. Showing that E(Y|X) = (1/2)(X+1) and E(Y) = 3/4 is straightforward. What I'd like to do is calculate E(Y^2) using E(Y^2|X)..... but I'm not sure how to do so: Y^2 is not uniformly distributed on Any...

probability

Nov 19, 2009
You have a coin, a pyramid, and a die. The coin has the numbers 1 and 2 on it, the pyramid has the numbers 1, 2, 3, 4 written on it, and the die has the usual 1 through 6 on it. An item is chosen at random and flipped/rolled. The coin has probability...

element

Nov 19, 2009
Suppose G has order 33. Show that it contains an element of order 3. So G can contains elements of order 3,11, and 33. If G contains an element of order 33, then this will generate the whole group. So suppose G contains no element of order 33. Then...

You know you're a math geek when...

Nov 17, 2009
... you accidentally misread "northern lights" as "noetherian lights" and start thinking about DCC. ... you squirt mayonnaise on your sandwich in the shape of an aleph. ... you post such exploits on an online math community. ... you add to this...

CS Grad School Advice -- What to choose as a field of interest?

Nov 16, 2009
I couldn't find an active Computer Science LJ and figured there were some CS students here =), so here goes: I'm applying to computer science graduate schools, but I'm not sure what subfield (e.g., AI, Theory, Computer Architecture) to talk about in...


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