MS Module 23 Balance principle multiplicative model practice exam questions
(The attached PDF file has better formatting.)
The mean values and the number of observations in each cell of a 2 × 2 classification table are
Means Column 1 Column 2 Observations Column 1 Column 2
Row 1 87 45 Row 1 14 16
Row 2 31 15 Row 2 19 15
Illustration: The cell in row 1 column 1 has a mean of 87 from a sample of 14 observations.
An actuary is setting class relativities for insurance pricing using a multiplicative model balance principle, with
● a base rate of 10
● a starting relativity for column 1 of 2.1
● a starting relativity for column 2 of 1
Question 23.1: Balance principle multiplicative model implied relativity row 1
What is the implied relativity for Row 1, given the starting relativities by column?
Answer 23.1: (87 × 14 + 45 × 16) / (10 × (2.1 × 14 + 1.0 × 16) ) = 4.269
(implied relativity for row 1 = observed value for row 1 / expected value for row 1 with no relativity)
Question 23.2: Balance principle multiplicative model implied relativity row 2
What is the implied relativity for Row 2, given the starting relativities by column?
Answer 23.2: (31 × 19 + 15 × 15) / (10 × (2.1 × 19 + 1.0 × 15) ) = 1.483
(implied relativity for row 2 = observed value for row 2 / expected value for row 2 with no relativity)
Question 23.3: Balance principle multiplicative model implied relativity column 1
What is the implied relativity for Column 1, given the computed relativities by row?
Answer 23.3: (87 × 14 + 31 × 19) / (10 × (4.269 × 14 + 1.483 × 19) ) = 2.055
(implied relativity for column 1 = observed value for column 1 / expected value for column 1 with no relativity)
Question 23.4: Balance principle multiplicative model implied relativity column 2
What is the implied relativity for Column 2, given the computed relativities by row?
Answer 23.4: (45 × 16 + 15 × 15) / (10 × (4.269 × 16 + 1.483 × 15) ) = 1.044
(implied relativity for column 2 = observed value for column 2 / expected value for column 2 with no relativity)
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