Actuarial Outpost calculating expected value
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 Probability Old Exam P Forum

#1
10-05-2018, 11:07 AM
 kn005 Member Join Date: Jul 2010 Favorite beer: I don't drink beer!! Johnny Walker Black Label it is Posts: 346
calculating expected value

I have a question on how to calculate expected values when you have ranges so for eg.

probability
less than 50 27%
50- 69 14%
70- 89 15%
90 or more 47%

how do you calculate the expected value when you have ranges? do you use the midpoint for each range and multiply by the probability?

Last edited by kn005; 10-05-2018 at 11:28 AM..
#2
10-05-2018, 11:25 AM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 3,689

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#3
10-05-2018, 11:28 AM
 kn005 Member Join Date: Jul 2010 Favorite beer: I don't drink beer!! Johnny Walker Black Label it is Posts: 346

Quote:
oops i'll change it. It was just a quick example. do you use the midpoint though?
#4
10-05-2018, 12:25 PM
 kn005 Member Join Date: Jul 2010 Favorite beer: I don't drink beer!! Johnny Walker Black Label it is Posts: 346

Also, how do i find the midpoint of 90 or more?
#5
10-05-2018, 12:27 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,338

I don't think you can estimate the mean with an open ended interval unless you assume a parametric distribution, estimate parameters, and then do a chi square test to test the fit of the model.
#6
10-05-2018, 12:42 PM
 ShundayBloodyShunday Member CAS Join Date: Apr 2013 Posts: 2,151

Quote:
 Originally Posted by kn005 oops i'll change it. It was just a quick example. do you use the midpoint though?
Quote:
.

What is the support of the underlying data? For example, are these test scores--so support on the interval [0, 100]? Or temperature (in degrees F) in Phoenix, AZ--so support on the interval [40, 110]?

It is completely reasonable to use midpoints (absent all other information) since that is the implicit assumption of uniform-distribution within a given interval.