Skip to content

IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples

Which change would, on its own, reduce the standard error of a Monte Carlo estimate of a mean without increasing the number of simulations?

Using antithetic variates reduces the standard error. Pairing each run with a negatively correlated counterpart lowers the variance of the pair average compared with independent runs. Changing the seed, rounding outputs or reusing one uniform number does not improve accuracy, and reusing the number actually ruins the estimate.

  1. AUsing antithetic variates that give negatively correlated paired outputsCorrect
  2. BUsing a different seed for the random number generator
  3. CReporting the sample median instead of the mean
  4. DUsing the same uniform number for every run
  5. Rounding all outputs to the nearest whole rupee

Explanation

Antithetic variates pair runs with negative correlation, so the average of each pair has lower variance than two independent runs. A different seed changes the sample but not its variability. Using the same uniform in every run would destroy independence and give no information.

Did you get it right without looking?

One question tells you little. A timed set on Basic univariate distributions and generating samples shows your real accuracy, how long you take and where you lose marks.

Practise Basic univariate distributions and generating samplesFree diagnostic mock

More Basic univariate distributions and generating samples questions