0

It is given that the probability that one among two radioactive atoms will decay in an interval $x,x+dx$ and another one will decay in a time interval $y+dy$ is given by the following expression: $$Ne^{-y\alpha-x\beta-\gamma\sqrt{xy}}dydx$$ where $\alpha, \beta>0$, and $\gamma~\epsilon~R$.

How can I determine the expected value and standard deviation of decay time for both atoms in analytical form? Also, how do I numerically calculate the approx. probability that one of them decays prior to the other?

Spoilt Milk
  • 361
  • This is just a joint distribution. What is the research interest? – Douglas Zare Oct 27 '17 at 13:57
  • I wanted to generalize this to a n-radioactive chain with decay happening at definite $\delta t$ intervals, but was stuck at the initial part of it. – Spoilt Milk Oct 27 '17 at 14:42
  • well, you just integrate over $x$ to get the marginal distribution of $y$, and if you want to know the probability that $x$ decays before $y$ you integrate over over $x$ from $0$ to $y$ and then over $y$ from $0$ to $\infty$. (no closed form expression, this is an integral you'll need to evaluate numerically) – Carlo Beenakker Oct 27 '17 at 16:55

0 Answers0