Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

Alpha particles are emitted by a radio active source at an average rate of $5$ in a $20$ minutes interval.Using poisson distribution find the probability that there will be at least $2$ emission in a particular $20$ minutes interval .$[e^{-5}=0.0067].$

Can you answer this question?

1 Answer

0 votes
  • A random variable $X$ is said to have a poisson distribution if the probability mass function of $X$ is
  • $P(X=x)=\large\frac{e^{\Large -\lambda }\lambda^x}{x!}$$\qquad (x=0,1,2........$ for some $\lambda > 0)$
  • Constants of a poisson distribution :
  • Mean=Variance=$\lambda$
  • The parameter of the Poisson distribution is $\lambda$
  • A Poisson random variable corresponds to rare events.
Step 1:
Let $X$ be the random variable denoting the number of alpha particles emitted in a 20 minutes interval .
$X$ follows a poisson distribution with mean =5 particles in a 20 minutes interval.
$\therefore \lambda=5$
$X\sim P(5)$
$P(X=x)=\large\frac{e^{-5}5^x}{x!}$$\quad x=0,1,2.........$
Step 2:
Probability of at least 2 emissions in a 20 minutes interval
$P(X\geq 2)=1-P(X<2)$
answered Sep 18, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App