2 A radioactive source is decaying at a mean rate of 3.4 counts per 5 seconds.
- State conditions for a Poisson distribution to be a suitable model for the rate of decay of the source.
You may assume that a Poisson distribution with a mean rate of 3.4 counts per 5 seconds is a suitable model.
- State the variance of this Poisson distribution.
- Find the probability of
(A) exactly 3 counts in a 5 -second period,
(B) at least 3 counts in a 5 -second period. - Find the probability of exactly 40 counts in a period of 60 seconds.
- Use a suitable approximating distribution to find the probability of at least 40 counts in a period of 60 seconds.
- The background radiation rate also, independently, follows a Poisson distribution and produces a mean count of 1.4 per 5 seconds. Find the probability that the radiation source together with the background radiation give a total count of at least 8 in a 5 -second period.