IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
Two independent Uniform(0,1) values u1 = 0.5 and u2 = 0.8 are used in the Box-Muller transform to generate Z = sqrt(-2 ln u1) cos(2π u2). Which value is closest to Z?
Z is approximately 0.36. The radius term sqrt(-2 ln 0.5) is about 1.177, and cos(2π x 0.8) equals cos 288 degrees, which is about 0.309; their product is about 0.364.
- A-1.18Correct
- B-0.36
- C0.36
- D1.18
- -1.60
Explanation
sqrt(-2 ln 0.5) = sqrt(1.3863) = 1.1774. cos(2π x 0.8) = cos(288°) = cos(72°) = 0.3090. The product is 0.3638, so the closest value is 0.36 and the keyed option must be that value.
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