Question

(a) Define the properties of a homogeneous Poisson process. Include a conceptual diagram illustrating the process, and label

(c) Describe how the following distributions are related to a homogeneous Poisson process with rate A Poisson(A) f(x) x0 At E

(a) Define the properties of a homogeneous Poisson process. Include a conceptual diagram illustrating the process, and label the diagram to support your answer. [3 marks How is an inhomogeneous Poisson process different? [1 marks (b)
(c) Describe how the following distributions are related to a homogeneous Poisson process with rate A Poisson(A) f(x) x0 At Exponential(A) f(x) λαp f(x) AexpAt At)- (n-1 Gamma(n, A) Your description should identify what each distribution is used to model, and should include at least one conceptual diagram similar to the one used in part (a) 3 marks
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