Use numerical methods to find the extinction probability for a branching process with Poisson offspring distribution with parameter 𝜆=1.5. A branching process has offspring distribution with a 0 =p,...

Use numerical methods to find the extinction probability for a branching process with Poisson offspring distribution with parameter 𝜆=1.5.

A branching process has offspring distribution with a₀=p, a₁
= 1−p−q, and a₂
= q. For what values of p and q is the process supercritical? In the supercritical case, find the extinction probability.