The probability that a certain radioactive mass emits no particles in a one-minute time period is 0.1353. What is the mean number of particles emitted per minute?

From the above I was able to deduce that P(X>=1) is 1 - 0.1353 = 0.8647.

0.8647 chance of at least 1 particle being emitted in a minute.

I'm not sure how to calculate the mean number of particles per minute though.


What do you know? You know that P(X = 0) = 0.1353. correct? What does the probability mass function of a Poisson distribution look like? $P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}$ Since you can punch in P(X = 0) = .1353 for k = 0, you can back out the lambda value. Now what is the mean of a Poisson distribution? I'll leave that up to you....

  • $\begingroup$ Thank you very much. I came up with the same revelation right before you posted. I came up with lambda = 2.000261 as the mean. Thanks for the confirmation. $\endgroup$ – itsSLO Feb 7 '14 at 19:42
  • $\begingroup$ itsSLO - looks right to me $\endgroup$ – Glen_b -Reinstate Monica Feb 7 '14 at 23:59
  • $\begingroup$ what does k represent in Poisson's formula? $\endgroup$ – Kristof Tak Aug 1 '15 at 13:44
  • $\begingroup$ in this case, k represents a certain number of arrivals or events occurring over a certain period of time. Since the person wanted to know the $\lambda$ value, and knew the answer for k = 0, then it should be easy to back out the answer he/she needed. $\endgroup$ – Eric Peterson Oct 28 '15 at 18:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.