# Poisson distribution

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....
• what does k represent in Poisson's formula? – Kristof Tak Aug 1 '15 at 13:44
• 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. – Eric Peterson Oct 28 '15 at 18:30