Answer to Question #168449 in Statistics and Probability for Christina

Question

When studying cesium 137, it is found that during the course of decay over 365 days, 1,000,000 radioactive atoms are reduced to 977,287 radioactive atoms. Find its variance

Answer 1

By defination The poisiion distribution is a discrete probability distribution that express the probability of given number of events occuring in a fixed interval of time and space if these events occur with a known average rate and indepedntly of the time since the last event. If $\mu$ is the known average rate of occureence , then the probability that exactly x success occur is given by-

$P=\dfrac{\mu^K e^{-u}}{x!}$

Where c in the Eulerian number Whose approximate value is 2.71828. The mean and variance of a possion distribution are both given by $\mu.$

Number of atom decays in 365 days= 1000000-977287=22713

Mean number of decays = $\dfrac{22713}{365}=62.2274\text{ decay/day}$

Since variance and mean are equal in Possion distribution-

Variance =$62.2274$