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henktijms
Topic Author
Posts: 34
Joined: December 25th, 2010, 2:50 pm

How to choose your numbers?

July 11th, 2018, 5:18 pm

On each of 100 blank cards you have to put one of the numbers 1, 2, 3, 4 or 5. If this has been done, one of the cards is randomly drawn.You have to pay in dollars the same amount as the number on the card drawn. How to put  your numbers on the cards in order to minimize the  maximum  of  $E(X_1)\ldots, E(X_5)$, where the random variable $X_k=1$ if the number on the  drawn card is $k$ and $X_k=0$ otherwise?
 
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ppauper
Posts: 69083
Joined: November 15th, 2001, 1:29 pm

Re: How to choose your numbers?

July 12th, 2018, 2:26 pm

there's too many paths to consider ([$]X_{1}=1,2,3,4,5[$] same for [$]X_{2}[$] etc)
I'll just write 1 on every card and owe $1
 
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Collector
Posts: 3923
Joined: August 21st, 2001, 12:37 pm

Re: How to choose your numbers?

September 11th, 2018, 11:49 pm

i write 5, but there were no rules about in addition putting - in front, so now you own me $5 per draw. I take cash only! After u pay me I will give $1 to ppauper so also he can play one round. I like to do Charity! Keeps almost everyone happy!

"1, 2, 3, 4 or 5."

commas clearly allowed, a flipped comma moved a tad up looks like a minus sign.
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