Hey,
I need some help with the following exercise (big test on Sunday).
Q: A lab researching cancer cells found that transformed epithelial cells divide at a rate of 5 divisions/hour.
1) What is the probability that in four hours, the cells will divide 25 times?
Lamda = 5/hour. P(X=25) = e^(-20) x (20^25)/(25!) = 0.0445. No problems so far.
2) Researchers saw that over four hours, the cells divided 22 times. What is the probability that 7 divisions occurred in the first hour?
This is what I have no idea how to calculate.
The answer is 0.139.
Thanks!!!
Hey Dason,
Thank you for your fast reply! 22 divisions in four hours - we'd expect 5.5 an hour... Don't know if it's the stress or lack of knowledge but I just can't figure it out
By the way, this isn't homework I need to hand in or anything... this is just me trying to learn for a big test and not quite succeeding.
Note that there are 22 divisions in total in the four hours. So what are the possible number of divisions in the first hour?
I don't have emotions and sometimes that makes me very sad.
Well, it could be anything between 0 and 22. So there are 23 possibilities.
What distribution(s) do you know that take support only a finite number of possibilities (between 0 and N - which is 22 in this case).
I don't have emotions and sometimes that makes me very sad.
Well, there's binomial and uniform - but what will the probability be? At first I thought it was 1/5.5 or 1/5 but that doesn't make much sense. Doing the binomial for x=7 when X~B(22, 0.2) didn't work out. I know I'm missing something elementary here and feel quite stupid to be honest.
You only looking at 1 hour out of the 4 total hours. So in that time you would expect 1/4 of the divisions to take place in that hour.
I don't have emotions and sometimes that makes me very sad.
Ok, I expect 5.5 and there's 7. P(X=7), E(X)=5.5, N=22. But I still don't understand which probability to use.
HadasL (10-01-2013)
You can actually use conditional probability and the independent increment property of Poisson process to calculate it.
Let be the number of divisions in the first hour, and be the number of divisions in the first 4 hours.
By the independent increment property, and are independent, as is the number of divisions in the last 3 hours.
For ,
and let you fill the remaining parts.
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