Actuarial Outpost Need help for this question
 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

 DW Simpson & CoWorldwide ActuarialRecruitment Entry Level JobsCasualty, Health, Life, Pension,Investment --Insurance / Consulting Asian JobsHong Kong, China, India, Japan, Korea, Indonesia, Singapore,Malaysia, and more Registration FormBe Notified of New Actuarial Jobs

 Thread Tools Display Modes
#1
08-14-2005, 05:58 PM
 cyc Member CAS Join Date: May 2005 Posts: 346
Need help for this question

Let X1 and X2 form a random sample from a Poisson distribution. The Poisson distribution has a mean of 1. If Y = min(X1, X2), then P(Y=1) = ?

In the answers, it says
P(Y=1) = P[(X1=1) intersection (X2 >= 1) ] + P[ (X2=1) intersection (X1 >=2)]

The part that I dont' understand is why in the second part of the equation, X1 >= 2? isn't it supposed to be >= 1 ?

By the way, the answer is (2e-3)/e^2

Thanks
#2
08-14-2005, 06:11 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,452

This part
Quote:
 In the answers, it says P(Y=1) = P[(X1=1) intersection (X2 >= 1) ] + P[ (X2=1) intersection (X1 >=2)]
is right. I didn't try to plug in the values to get the answer in terms of e.

To express the answer as the sum of two probabilities, you don't want any overlap. In this case, you are counting the case X1 = X2 = 1 in the first expression, so you must be sure to exclude it from the second.

 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 12:34 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