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Help with S2 question!!

Could someone please help me with 8b please? The answer is 0.206 particles per second
Reply 1
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swagmister
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Probability is 0.8. Look at poisson tables for 0.8 where P(X<<1) = 0.8. Find the Y
It's a good idea to write down what you're distribution is. You want X to be "the number of emissions in 4 seconds", you know there is 1 per second, so in 4 seconds there's going to be 4. So X~po(4)

I'm not sure what you've done there, but the poisson distribution formula is P(X=x)=e−λ(λ)xx! P(X=x) = \frac{e^{-\lambda}(\lambda)^{x}}{x!}
Reply 4
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swagmister
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Original post by Teleport1
Probability is 0.8. Look at poisson tables for 0.8 where P(X<<1) = 0.8. Find the Y


0.8 isn't in the tables
Reply 5
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swagmister
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Original post by NotNotBatman
It's a good idea to write down what you're distribution is. You want X to be "the number of emissions in 4 seconds", you know there is 1 per second, so in 4 seconds there's going to be 4. So X~po(4)

I'm not sure what you've done there, but the poisson distribution formula is P(X=x)=e−λ(λ)xx! P(X=x) = \frac{e^{-\lambda}(\lambda)^{x}}{x!}


I used used the formula for P(X=0) and P(X=1) then added them which would equal 0.8?
Original post by swagmister
I used used the formula for P(X=0) and P(X=1) then added them which would equal 0.8?


then divide by 4
Reply 7
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swagmister
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Original post by Teleport1
then divide by 4


Divide P(X=0)+P(X=1) by 4 before making it equal 0.8?
Original post by swagmister
Divide P(X=0)+P(X=1) by 4 before making it equal 0.8?


The above answer shouldnt be the right answer. Something is messed up. Try putting the given Y answer back into the formula to see if you get 0.8 which you shouldnt
Reply 9
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swagmister
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Original post by Teleport1
The above answer shouldnt be the right answer. Something is messed up. Try putting the given Y answer back into the formula to see if you get 0.8 which you shouldnt


Yep dividing P(X<<1) by 4 gives an imaginary number. I'm not sure where I've gone wrong with the working out I've shown
Original post by swagmister
Yep dividing P(X<<1) by 4 gives an imaginary number. I'm not sure where I've gone wrong with the working out I've shown


No i mean the answer of 0.206 is wrong. If you try to work backwards by putting it into the formula with x=1, it doesnt give anything close to 0.8 whether you divide/multiply by 4 or not. So their answer is most likely wrong
Original post by Teleport1
No i mean the answer of 0.206 is wrong. If you try to work backwards by putting it into the formula with x=1, it doesnt give anything close to 0.8 whether you divide/multiply by 4 or not. So their answer is most likely wrong


It does give 0.8 because you have to times 0.206 by 4 as the probability of 0 and 1 was for 4 seconds
I didn't see that the emission rate changes, what you have done is right up to the third line, but you can't take natural logs to one term, it must be all of it. I would suggest multiplying through by eλe^{\lambda} , but then you get an equation with a λ\lambda term as well, which I can only think of solving right now by iterative methods. It is 0.824... , then just divide it by 4.
Original post by NotNotBatman
I didn't see that the emission rate changes, what you have done is right up to the third line, but you can't take natural logs to one term, it must be all of it. I would suggest multiplying through by eλe^{\lambda} , but then you get an equation with a λ\lambda term as well, which I can only think of solving right now by iterative methods. It is 0.824... , then just divide it by 4.


Oh right I'm still not sure how I would go about solving it though
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