MTH 223: Mathematical Risk Theory
Tutorial 4
1. Provide N with the following distribution:
P[N = 0] = p0 = 0.2, P[N = 1] = p1 = 0.3; P[N = 2] = p2 = 0.3; P[N = 3] = p3 = 0.2.
Find the probability generating function of N and use it to find the mean and variance of N.
2. You are given that N is a member of the (a, b, 0) class of distribu- tions, and p0 = 0.4096, p1 = 0.4096 and p2 = 0.1536. Determine the distribution of N.
3. A Poisson random variable has parameter λ = 1.
(a) Find p0, p1 and p2 and the mean and variance for the zero-truncated version of this distribution.
(b) Find p0, p1 and p2 and the mean for the zero-modified version of this distribution with = 0.5.
4. The Independent Insurance Company insures 25 risks, each with a 4% probability of loss. The probabilities of loss are independent. On aver- age, how often would 4 or more risks have losses in the same year?