First passage time

How long until a particle diffuses to $x$? - Question given a population of diffusing particles, what is the probability distribution of first passage times ($\text{FPT}(x,t)$) to position $x?$ Typically this is found by solving the diffusion differential equation to find the probability distribution, integrating that to find the survival, and then differentiating that to find the $\text{FPT}$…