I think your definition of the subscripts in life contingencies is backwards. nPx would be life aged x surviving for n more years, no? So that you would be starting at x and ending at x + n.
There’s actually a reason for the Fisher Information shortcut. 1/FisherInfo is the Rao Cramer Lower Bound, and a lot of the common distributions/estimators that get used in the questions (but not all) are estimators that are minimum-variance unbiased estimators, and they usually hit the Rao Cramer Lower Bound. In other words, Var(theta_hat) = 1/Fisher a lot of the time which means Fisher = 1/Var(theta-hat).
Your statement on the F test for comparing the variances of two samples is incorrect. S_x^2/S_y^2 is distributed as [Chi-sq(n-1)/(n-1)]/[Chi-sq(m-1)/(m-1)], not Chi-sq(n-1)/Chi-sq(m-1). The F distribution is not the ratio of two chi squareds, but rather two chi squareds each divided by their number of degrees of freedom. The test statistic is correct, however, since S_x^2/sigma^2 is distributed as Chi-sq(n-1)/(n-1), and similarly for S_y^2.
I always forget that darn scaling, thanks Lila! For others who want a walkthrough of what Lila is pointing out, I walk through the derivation (without this mistake :) ) here: ruclips.net/video/uFSKhvrCGKI/видео.html&ab_channel=TheActuarialDataScientist
I think your definition of the subscripts in life contingencies is backwards. nPx would be life aged x surviving for n more years, no? So that you would be starting at x and ending at x + n.
You are 100% correct, thanks for catching that! I'll add a comment on this in the description of the video. Thanks Bahaa!
Am taking MAS-I later today, thank you for the quick review!
Taking exam in 2 days. Thanks for the help!!!!!
Note, Kernels are also almost always on every exam. Triangular, rectangular, and/or gaussian
Failed last time. Hopefully 2nd times a charm
Thank you for posting this! I am writing MAS 1 tomorrow :)
My pleasure! I am as well, best of luck to the both of us!
How was your Exam?
Thanks for creating!!! :)
Absolutely, my pleasure!
There’s actually a reason for the Fisher Information shortcut. 1/FisherInfo is the Rao Cramer Lower Bound, and a lot of the common distributions/estimators that get used in the questions (but not all) are estimators that are minimum-variance unbiased estimators, and they usually hit the Rao Cramer Lower Bound. In other words, Var(theta_hat) = 1/Fisher a lot of the time which means Fisher = 1/Var(theta-hat).
23:56 Thanks for the insight Kyle!
1000 (^2Ax) is the second moment of the present value random variable - needed if you ant to get the variance of the PV of the insurance.
Your statement on the F test for comparing the variances of two samples is incorrect. S_x^2/S_y^2 is distributed as [Chi-sq(n-1)/(n-1)]/[Chi-sq(m-1)/(m-1)], not Chi-sq(n-1)/Chi-sq(m-1). The F distribution is not the ratio of two chi squareds, but rather two chi squareds each divided by their number of degrees of freedom. The test statistic is correct, however, since S_x^2/sigma^2 is distributed as Chi-sq(n-1)/(n-1), and similarly for S_y^2.
I always forget that darn scaling, thanks Lila! For others who want a walkthrough of what Lila is pointing out, I walk through the derivation (without this mistake :) ) here: ruclips.net/video/uFSKhvrCGKI/видео.html&ab_channel=TheActuarialDataScientist
what site is this? TIA?