Recalling that P0(t) e t, check that P1(t) te t is a solution of your equation with initial condition P1(0) 0 The probabilities for the Poisson distribution can be derived by solving differential equations Let Pi (t) be the probability of exactly i events by time t, assuming an underlying rate of ...

Recalling that P0(t) = e-t, check that P1(t) = te-t is a solution of your equation with

Question:

Recalling that P0(t) = e-λt, check that P1(t) = λte-λt is a solution of your equation with initial condition P1(0) = 0.
The probabilities for the Poisson can be derived by solving differential equations. Let Pi (t) be the probability of exactly i events by time t, assuming an underlying rate of λ.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...