# Poisson

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#1
Hey, for part a I put that there are only two possible outcomes, that a pixel is dead or not, and this occurs independently therefore the binomial would be appropriate. However they also occur randomly and at a uniform average rate of occurrence of 1 in 500,000, and seen as they are independent the poisson is suitable. Is this correct ? Also, for part b I did Lamda = 1 x 2304/500 , therefore P(X=4) = 0.187331 using general poisson formula. I used the cumulative function on my calculator for P(X>4), however I'm not at all sure how to do part c and d. Any help would be greatly appreciated. Thanks
Last edited by RLangdon569; 1 month ago
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#2
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1 month ago
#3
The probability of at least 1 dead pixel is 1 - p(no dead pixels).
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#4
(Original post by DFranklin)
The probability of at least 1 dead pixel is 1 - p(no dead pixels).
so probability of finding one dead pixel is ( 1- ( 499,999/500,000)^n) ?
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1 month ago
#5
(Original post by RLangdon569)
so probability of finding one dead pixel is ( 1- ( 499,999/500,000)^n) ?
Ayup.
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#6
(Original post by DFranklin)
Ayup.
Hi
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#7
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#8
for part d, I am trying to do (1-(4+k/52+k)) x ( 4+k/52+k) = 8/81
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1 month ago
#9
(Original post by RLangdon569)
for part d, I am trying to do (1-(4+k/52+k)) x ( 4+k/52+k) = 8/81
Agreed.

Rearrange to a quadratic, and solve.
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#10
(Original post by ghostwalker)
Agreed.

Rearrange to a quadratic, and solve.
I tried that but I seem to get non-integer answers.
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#11
(Original post by RLangdon569)
I tried that but I seem to get non-integer answers.
48/(52+k) x 4+k/52+k = 8/81.

192+48k = 8/81 x ( k^2 + 104k + 2704)

K^2 - 868k + 760 = 0
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1 month ago
#12
(Original post by RLangdon569)
for part d, I am trying to do (1-(4+k/52+k)) x ( 4+k/52+k) = 8/81
I know this is like King Canute trying to roll back the tide, but what you've just written is actually completely wrong, because

(4+k/52+k) is the same as (remember division has higher precendence than addition).

What you meant is (4+k)/(52+k), which equals .

[To be clear, ghostwalker knows this: we're just all so used to people doing this wrong that we correct for it. The forum guidelines actually state that you should do this correctly - it just often feels like a lost cause).
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1 month ago
#13
(Original post by RLangdon569)
48/(52+k) x 4+k/52+k = 8/81.

192+48k = 8/81 x ( k^2 + 104k + 2704)

K^2 - 868k + 760 = 0
In red's in error - have another go.
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#14
(Original post by ghostwalker)
In red's in error - have another go.
Got it! Thank you . k=2 or 380
Last edited by RLangdon569; 1 month ago
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#15
(Original post by RLangdon569)
To check, do I use lamda = 2304/500 for the poisson in this question ?
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1 month ago
#16
(Original post by RLangdon569)
Got it! Thank you . k=2 or 380
Agreed.

Do take on board DFranklin's comments in post #12. Aside from being wrong, it's confusing from the helper's point of view, though I know what you meant in this case. But also, if what you're thinking and what you're writing are not consistent with each other, it can easily become a source of confusion for yourself, without you even realising it.
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#17
(Original post by ghostwalker)
Agreed.

Do take on board DFranklin's comments in post #12. Aside from being wrong, it's confusing from the helper's point of view, though I know what you meant in this case. But also, if what you're thinking and what you're writing are not consistent with each other, it can easily become a source of confusion for yourself, without you even realising it.
Definitely, it will not happen in the future. Thank you both for all of your help!
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#18
(Original post by RLangdon569)
To check, do I use lamda = 2304/500 for the poisson in this question ?
I am just now doubting myself a bit
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#19
I have used lamda=2304/500 to calculate both of the probability in part b

(Original post by ghostwalker)
Agreed.

Do take on board DFranklin's comments in post #12. Aside from being wrong, it's confusing from the helper's point of view, though I know what you meant in this case. But also, if what you're thinking and what you're writing are not consistent with each other, it can easily become a source of confusion for yourself, without you even realising it.
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1 month ago
#20
(Original post by RLangdon569)
I have used lamda=2304/500 to calculate both of the probability in part b
Agreed.
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