Actuarial Outpost elementary coin game problem
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#1
04-14-2006, 01:45 PM
 Phil Site Supporter Site Supporter Join Date: Sep 2001 Location: not on board the Enterprise Posts: 5,664
elementary coin game problem

Fair coin

You can play a game

Keep flipping the coin

until you get "tails"

Number of "heads" that you saw is how much \$\$\$ you win

E.g.

What's the expected value of this game
#2
04-14-2006, 01:50 PM
 carrot Class Clown SOA Join Date: Jan 2003 Location: dirt Studying for the eye exam Posts: 9,565

Isn't that the negative binomial distribution? I don't remember the expected value, though. I think it was something like 1/p? If so, then 1/.5 give you an expected value of \$2.
#3
04-14-2006, 01:52 PM
 3rookie Member Join Date: Nov 2001 Posts: 9,486

1
#4
04-14-2006, 01:53 PM
 Da Bears! Member CAS Join Date: May 2005 Location: Chicago Favorite beer: Birch Posts: 7,618

Sounds geometric to me.....\$1
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#5
04-14-2006, 01:54 PM
 Dr T Non-Fan Member Join Date: Sep 2001 Location: Just outside of Nowhere Posts: 59,703

What's wiki's solution? I think we could discuss this for 400 posts or so.
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#6
04-14-2006, 01:59 PM
 Da Bears! Member CAS Join Date: May 2005 Location: Chicago Favorite beer: Birch Posts: 7,618

Quote:
 Originally Posted by mlschop negative binomial expected value is r times Beta. this is geometric since you are looking for first loss, so r = 1. Isn't Beta probability of success, so it's 0.5, so wouldn't the E[X] = 0.5? where is everyone getting 1?
If you succeed on the first attempt, you continue for another attempt. So.....E[X] = 1/2 + 1/4 + 1/8 + 1/16....ya know, GEOMETRIC.

Somebody hasn't passed Course 1 yet....
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#7
04-14-2006, 02:00 PM
 DeepPurple Member Join Date: Jun 2004 Posts: 2,640

Who would want a car over a goat anyway. A car can take you places, but a good goat can give you love.
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#8
04-14-2006, 02:03 PM
 carrot Class Clown SOA Join Date: Jan 2003 Location: dirt Studying for the eye exam Posts: 9,565

Quote:
 Originally Posted by Da Bears! Sounds geometric to me.....\$1
Yeah, that's what I meant.
#9
04-14-2006, 02:04 PM
 carrot Class Clown SOA Join Date: Jan 2003 Location: dirt Studying for the eye exam Posts: 9,565

Quote:
 Originally Posted by DeepPurple Who would want a car over a goat anyway. A car can take you places, but a good goat can give you love.
ATGTFWG.
#10
04-14-2006, 02:10 PM
 Happy Eellike Prodigality Member Join Date: Mar 2005 Posts: 1,576

stop it

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