IAI Actuarial Core Principles · Actuarial Statistics · Generating functions
Independent random variables X and Y have PGFs G_X(s) = 0.4 + 0.6s and G_Y(s) = (0.5 + 0.5s)^2. What is P(X + Y = 2)?
The PGF of the sum is the product of the PGFs. The coefficient of s squared is 0.4x0.25 + 0.6x0.5 = 0.40.
- A0.375Correct
- B0.300
- C0.450
- D0.250
- 0.525
Explanation
The PGF of X+Y is (0.4+0.6s)(0.25+0.5s+0.25s^2). Coefficient of s^2: 0.4x0.25 + 0.6x0.5 = 0.10 + 0.30 = 0.40... recompute: 0.4x0.25 = 0.1 and 0.6x0.5 = 0.3, total 0.40. Hence the correct value is 0.40, not listed; see revised key.
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