Actuarial Outpost Marginal of Conditional Binomial?
 User Name Remember Me? Password
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Registration FormBe Notified of New Actuarial Jobs D.W. Simpson & Company InternationalActuarialRecruiters www.dwsimpson.com Australia Jobs Casualty, Life,Superannuation, Health &Investment PensionActuarial JobsConsulting &Insurers --Students, Associates &Fellows

 Thread Tools Display Modes
#1
06-19-2012, 05:12 PM
 Xkhaos CAS Join Date: Nov 2011 Posts: 17
Marginal of Conditional Binomial?

Let X~Bin(n,p), Y|X=x~Bin(x,p*)
Is there a shortcut to get P(Y=y)?
I ask because I'm having trouble getting P(Y=y) through the use of
P(Y=y) = sum of all x of f(x,y), where f(x,y) = f(y|x)*f(x).
#2
06-19-2012, 06:30 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 1,365

This is a guess but it would seem that y would be binomial (n, pp*).
#3
06-19-2012, 07:03 PM
 daaaave David Revelle Join Date: Feb 2006 Posts: 2,488

Suppose you flip n coins, each of which is heads with probability p. Then X is the number of heads. Saying that (Y | X=x)~Bin(x, p*) means that we then flip X new coins, each of which is heads with probability p*, and Y is the number of heads on that second round. Then Y~Bin(n, pp*) because each original flip results in heads on the second round with probability pp*.
__________________

#4
06-19-2012, 09:45 PM
 asrauf Member CAS SOA Join Date: Mar 2012 Location: Canada Studying for Studying for MFE Posts: 33

Quote:
 Originally Posted by daaaave Suppose you flip n coins, each of which is heads with probability p. Then X is the number of heads. Saying that (Y | X=x)~Bin(x, p*) means that we then flip X new coins, each of which is heads with probability p*, and Y is the number of heads on that second round. Then Y~Bin(n, pp*) because each original flip results in heads on the second round with probability pp*.
Wonderful explanation Dave!
I passed P in May mainly through your well explained concepts...

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 04:09 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top