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Poisson

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

(edited 2 years ago)

The probability of at least 1 dead pixel is 1 - p(no dead pixels).

Reply 3

RLangdon569

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) ?

Reply 4

DFranklin

Original post by RLangdon569

so probability of finding one dead pixel is ( 1- ( 499,999/500,000)^n) ?

Ayup.

Reply 5

RLangdon569

Original post by DFranklin

Ayup.

for part d, I am trying to do (1-(4+k/52+k)) x ( 4+k/52+k) = 8/81

Reply 8

ghostwalker

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.

Reply 9

RLangdon569

Original post by ghostwalker

Agreed.

Rearrange to a quadratic, and solve.

I tried that but I seem to get non-integer answers.

Reply 10

RLangdon569

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

Reply 11

DFranklin

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

(4+\frac{k}{52} + k)

(remember division has higher precendence than addition).

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

\dfrac{4+k}{52+k}

.

[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).

Reply 12

ghostwalker

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.

Reply 13

RLangdon569

Original post by ghostwalker

In red's in error - have another go.

Got it! Thank you . k=2 or 380

(edited 2 years ago)

Reply 14

RLangdon569

Original post by RLangdon569

To check, do I use lamda = 2304/500 for the poisson in this question ?

Reply 15

ghostwalker

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.