ST 3246 Statistical Models for Actuarial Science – LumiNUS Quiz 1 (HW1), Singapore

Assignment Details:

Your student number has the format A 0 1 i j k m n I, where each of i, j, k, m, and n is a digit
from {0, 1, 2, . . . , 9}, and I is an alphabet from {A,B, C, . . . , Z}.
Let X have a lognormal distribution with parameters
µ = (−1)i × 0.1 × j and σ = 0.1 × i + 0.01 × j.
The parameters µ and σ are not to confused with the mean and standard deviation of the lognormal distribution.
Calculate (rounding your answer to four decimal places)
1. the kurtosis of X,
2. eX(d) with d = 1 + 0.02 × m, and
3. the standard deviation of the limited loss variable with u = 2 − 0.1 × n.
Use a spreadsheet or statistical program to evaluate Φ(·), the standard normal cdf; using a statistical table will not give you the required accuracy.