## measurement statistics

betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### measurement statistics

as a "would be" theoretician I left the counting statistics and lab method problems at the end and now look at me, I have found some difficulties:
ex:
An experimenter ( ) measures the counting rate from a radioactive source as 10150 counts in 100 minutes. Without changing any of the conditions, the experimenter counts for one minute. There is a probability of about 15% that the number of counts recorded will be fewer than
A 50
B 70
C 90
D 100
E 110

Now, this problem is a permutation of the problem where the number of counts is given and the probability is asked. My problem is that I don't know how to solve that problem either...

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: measurement statistics

betelgeuse1 wrote:as a "would be" theoretician I left the counting statistics and lab method problems at the end and now look at me, I have found some difficulties:
ex:
An experimenter ( ) measures the counting rate from a radioactive source as 10150 counts in 100 minutes. Without changing any of the conditions, the experimenter counts for one minute. There is a probability of about 15% that the number of counts recorded will be fewer than
A 50
B 70
C 90
D 100
E 110

Now, this problem is a permutation of the problem where the number of counts is given and the probability is asked. My problem is that I don't know how to solve that problem either...
the avg count <x>=10150/100=101.5 counts/sec now to calculate the std deviation (radioactive decay follow gaussian distribution) sigma=sqrt(<x>) which is approx 10 , now since the probability of the next count is 15%, this means this is just outside the 1 sigma region (which 68%) thus the counts recorded will be <x>+ /- sigma, since the question asks fewer then, this means we require the <x>-sigma ie 101.5-10~ 91 closest to C
also note that its 15% (<16%) thus the counts should be less than 91.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: measurement statistics

blackcat007 wrote:[ the avg count <x>=10150/100=101.5 counts/sec now to calculate the std deviation (radioactive decay follow gaussian distribution) sigma=sqrt(<x>) which is approx 10 , now since the probability of the next count is 15%, this means this is just outside the 1 sigma region (which 68%) thus the counts recorded will be <x>+ /- sigma, since the question asks fewer then, this means we require the <x>-sigma ie 101.5-10~ 91 closest to C
also note that its 15% (<16%) thus the counts should be less than 91.
You probably mean 101.5 counts per minute. The above analysis is absolutely correct for the case quoted but if the rate of disintegration is vanishingly small (but non-zero) it fails (Gaussian distribution is not the correct distribution to describe nuclear disintegration of vanishingly small rate). However, because gaussian is the easiest to remember this is why it is encountered so frequently in PGRE.
Last edited by physics_auth on Wed Sep 16, 2009 2:50 pm, edited 1 time in total.

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: measurement statistics

physics_auth wrote:
blackcat007 wrote:[ the avg count <x>=10150/100=101.5 counts/sec now to calculate the std deviation (radioactive decay follow gaussian distribution) sigma=sqrt(<x>) which is approx 10 , now since the probability of the next count is 15%, this means this is just outside the 1 sigma region (which 68%) thus the counts recorded will be <x>+ /- sigma, since the question asks fewer then, this means we require the <x>-sigma ie 101.5-10~ 91 closest to C
also note that its 15% (<16%) thus the counts should be less than 91.
You probably mean 101.5 counts per minute. The above analysis is correct for the case quoted but if the rate of disintegration is vanishingly small (but non-zero) it fails (Gaussian distribution is not the correct distribution to describe nuclear disintegration of vanishingly small rate). However, because gaussian is the easiest to remember this is why it is encountered so frequently in PGRE.
oh yeah sorry.. its counts/min..

I must mention my teacher 'physics_auth' who taught me this.. even i had left out this part for the end.. but with his beautiful description .. i could understand this..

betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### Re: measurement statistics

@ phys_auth: is that right? I was looking around the forum hoping to find some introduction to measurement statistics. Is there something like that? blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: measurement statistics

betelgeuse1 wrote:@ phys_auth: is that right? I was looking around the forum hoping to find some introduction to measurement statistics. Is there something like that? you can find something here http://www.fizika.org/skripte/of-prakt/5_2_05.pdf and here http://www.physics.sfsu.edu/~bland/cour ... b2/b2.html

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: measurement statistics

betelgeuse1 wrote:@ phys_auth: is that right? I was looking around the forum hoping to find some introduction to measurement statistics. Is there something like that? Well, I think that none undergraduate physicist is taught nuclear statistics unless they had choosen highly specialized courses in nuclear physics. This subject is a heavy one, thus I would advise that shouldn't spend time studying it, but learn a few stuff to be able to cope with some questions. You don't need to understand why sth is like this or that. The solution of Blackcat007 is correct.

betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### off topic

Not understanding why something is as it is, is very against my belief in physics. I had some success in studying physics by understanding why something is as it is... I had nuclear physics lectures (lots of them) but not from the experimental point of view... In my system you choose at the beginning of the college your "profile" (mathematical physics, pure physics, Medical physics, Engineering Physics) and I took "pure" physics. This is why I have some problems in dealing with experimental stuff... I know experimental things but I cannot really use them... Anyway, learning without understanding what we learn is called in my country "pre-exam syndrome" and it is said that in this condition a student can learn anything, something like hypnosis... physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: off topic

betelgeuse1 wrote:Not understanding why something is as it is, is very against my belief in physics. I had some success in studying physics by understanding why something is as it is... I had nuclear physics lectures (lots of them) but not from the experimental point of view... In my system you choose at the beginning of the college your "profile" (mathematical physics, pure physics, Medical physics, Engineering Physics) and I took "pure" physics. This is why I have some problems in dealing with experimental stuff... I know experimental things but I cannot really use them... Anyway, learning without understanding what we learn is called in my country "pre-exam syndrome" and it is said that in this condition a student can learn anything, something like hypnosis... This tactic is also against my belief in physics, and this is why I prolonged my undergraduate studies ... to gain a solid foundation about each subject taught in class, from general physics, ... to chaotic dynamics and general relativity. But the learning-without-understanding method "seems" to apply successfully to tests such as PGRE. I hope you understand now why I incite you to follow the "unorthodox route". On the other hand, you can spend all time till the exams to try to master nuclear statistics, but your "memory storage" may suffer in the end ... .

Last but not least, I was also taught nuclear physics, which was an extremely hard course to pass (let alone to earn a good grade), but time pressure enforces PGRE test takers to work in quick paces (and touch only superficially some things!). If you seriously want to learn this experimental stuff give me a notice to propose you a thoroughgoing book.

betelgeuse1
Posts: 116
Joined: Sat May 09, 2009 10:14 am

### Re: measurement statistics

nope! Right now I just want some info about how to use something that I don't understand... black box type numerology, nothing more!