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 =$62.2274$