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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: hyperblade01 on November 08, 2009, 07:23:18 pm

Title: Probability Notation
Post by: hyperblade01 on November 08, 2009, 07:23:18 pm
For binomial do we have to write for example:

X ~ Bi (6, 0.6)

or is it not necessary..
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For transitional matrices, how do we label the columns and rows?
Let's say it's one of those questions about rain and no rain

Is it alright to label it as R and N, saying what each mean on the side?
Or do we have to do the whole Pr(R|R') stuff...



Thanks in advance guys :)
Title: Re: Probability Notation
Post by: kdgamz on November 08, 2009, 07:35:21 pm
For binomial do we have to write for example:

X ~ Bi (6, 0.6)

or is it not necessary..
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it depends, u wudnt normally hav to do that, but if X is not defined in the question and in your answer u randomly pull X
out of nowhere, the assessors might get confused...i normally do use that notation

in short..i dont think u hav to do that, simply labelling the parameters (n=... p=...) wud probably be enough
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 07:36:11 pm
Nah you don't have to calc synatx, just simply state p = blah n = blah like kdgamz said.
Title: Re: Probability Notation
Post by: mankay on November 08, 2009, 07:55:24 pm
Nah you don't have to calc synatx, just simply state p = blah n = blah like kdgamz said.

Would the following be fine?

X~Bi(n,p)|X=number of people, etc
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 07:58:31 pm
Nah you don't have to calc synatx, just simply state p = blah n = blah like kdgamz said.

Would the following be fine?

X~Bi(n,p)|X=number of people, etc

I personally never use Calc syntax for probability, I just state the values of the variables and plug in calc. If the question was worth more than 1 mark, I write the formula out etc.
Title: Re: Probability Notation
Post by: kdgamz on November 08, 2009, 08:01:05 pm
Nah you don't have to calc synatx, just simply state p = blah n = blah like kdgamz said.

Would the following be fine?

X~Bi(n,p)|X=number of people, etc


u dont hav to be too specific, but if thats how u want to do it then....
Title: Re: Probability Notation
Post by: mankay on November 08, 2009, 08:28:09 pm
Nah you don't have to calc synatx, just simply state p = blah n = blah like kdgamz said.

Would the following be fine?

X~Bi(n,p)|X=number of people, etc

I personally never use Calc syntax for probability, I just state the values of the variables and plug in calc. If the question was worth more than 1 mark, I write the formula out etc.

I'm fairly certain none of what i wrote is calculator syntax (in other words, it's proper mathematical notation)
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 08:31:05 pm
Nah you don't have to calc synatx, just simply state p = blah n = blah like kdgamz said.

Would the following be fine?

X~Bi(n,p)|X=number of people, etc

I personally never use Calc syntax for probability, I just state the values of the variables and plug in calc. If the question was worth more than 1 mark, I write the formula out etc.

I'm fairly certain none of what i wrote is calculator syntax (in other words, it's proper mathematical notation)
Mathematical notation is to just simply state p and n.

And then write out the binomial formula and plug in the respective values.
Title: Re: Probability Notation
Post by: moekamo on November 08, 2009, 08:50:10 pm
Nah you don't have to calc synatx, just simply state p = blah n = blah like kdgamz said.

Would the following be fine?

X~Bi(n,p)|X=number of people, etc

I personally never use Calc syntax for probability, I just state the values of the variables and plug in calc. If the question was worth more than 1 mark, I write the formula out etc.

what formula can you use for normal and inverse normal, or do you shade the region of the curve or something?
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 08:55:34 pm
Nah you don't have to calc synatx, just simply state p = blah n = blah like kdgamz said.

Would the following be fine?

X~Bi(n,p)|X=number of people, etc

I personally never use Calc syntax for probability, I just state the values of the variables and plug in calc. If the question was worth more than 1 mark, I write the formula out etc.

what formula can you use for normal and inverse normal, or do you shade the region of the curve or something?
You don't just simply state the value of the answer if it's 1 mark.

If more, then you state the probability ie, Pr(X>a) or whatever and then state the values of mean, and s.d.
Title: Re: Probability Notation
Post by: mankay on November 08, 2009, 09:12:48 pm
Mathematical notation is to just simply state p and n.

That is not standard mathematical notation at all.
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 09:16:04 pm
Mathematical notation is to just simply state p and n.

That is not standard mathematical notation at all.
Yes it is.

Tell me where you see Bi(n,p) that is not universal notation at all.



Stating the values of p and n is as simple as it gets and tells the examiner you clearly know what you are doing instead of some Bi(n,p) jibberish.
Title: Re: Probability Notation
Post by: arthurk on November 08, 2009, 09:17:49 pm
what about in the case of binomcdf
what do we write when we want to for example n=10 p=0.3 and we want Pr(X>4)
what should we write down?
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 09:20:30 pm
what about in the case of binomcdf
what do we write when we want to for example n=10 p=0.3 and we want Pr(X>4)
what should we write down?


Then plug into calc and write answer. (I'd think you can just plug into calc and write the answer straight away and just state you used your calculator.)

If it was Pr(X>4) and n = 200 then all you have to write is "Using TI-89 (whatever calculator you are using) binomialcdf" after you write your answer.

If it was Pr(X=4) then you'd write
Title: Re: Probability Notation
Post by: arthurk on November 08, 2009, 09:21:40 pm
awwww
sounds like binomial probability is pretty gay with working
Title: Re: Probability Notation
Post by: VeryCrazyEdu. on November 08, 2009, 09:22:08 pm
My teacher always told us to write the X~Bi(n,p) when x=

and then Pr(x=4)= blah blah blah

now im getting worried eeeeek
Title: Re: Probability Notation
Post by: arthurk on November 08, 2009, 09:23:31 pm
My teacher always told us to write the X~Bi(n,p) when x=

and then Pr(x=4)= blah blah blah

now im getting worried eeeeek

You shouldn't need to though i mean we can state the domain in many vcaa acceptable ways without the arrow R notation so i doubt they'd get too picky with this
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 09:23:54 pm
We've been told at school to just state the values of all the variables and then if you used calculator, write in brackets afterwards that you did.



And seriously, VCAA examiners are human, if you set your working out clearly, they will award you marks.
Title: Re: Probability Notation
Post by: GerrySly on November 08, 2009, 09:24:04 pm
I write...



Then the answer, that seems to get me around writing calculator syntax
Title: Re: Probability Notation
Post by: TheJosh on November 08, 2009, 09:25:29 pm
What if you just use PRCHEAT what do you write??
Title: Re: Probability Notation
Post by: arthurk on November 08, 2009, 09:27:16 pm
thats new notation to me
Will x only take whole numbers though? won't it include all the decimals in between?
Title: Re: Probability Notation
Post by: mankay on November 08, 2009, 09:49:21 pm

Yes it is.

Tell me where you see Bi(n,p) that is not universal notation at all.

I didn't use Bi(n,p) at all.

I said, X ~ Bi(n,p)|X=number of whatever.

That means X is a member of a binomial distribution where the mean is n and the probability of success is p; where X is the number of *whatever*. Of course this would follow with whatever is needed (e.g. Pr(X > 2), etc).
Title: Re: Probability Notation
Post by: mankay on November 08, 2009, 09:55:34 pm

Yes it is.

Tell me where you see Bi(n,p) that is not universal notation at all.

I didn't use Bi(n,p) at all.

I said, X ~ Bi(n,p)|X=number of whatever.

That means X is a member of a binomial distribution where the number of trials is n and the probability of success is p; where X is the number of *whatever*. Of course this would follow with whatever is needed (e.g. Pr(X > 2), etc).
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 10:05:31 pm
thats new notation to me
Will x only take whole numbers though? won't it include all the decimals in between?
Nah for summation notation, the values it takes is an element of . To be pedantic you can specify , but this is implied.
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 10:07:18 pm

Yes it is.

Tell me where you see Bi(n,p) that is not universal notation at all.

I didn't use Bi(n,p) at all.

I said, X ~ Bi(n,p)|X=number of whatever.

That means X is a member of a binomial distribution where the mean is n and the probability of success is p; where X is the number of *whatever*. Of course this would follow with whatever is needed (e.g. Pr(X > 2), etc).
yeah ok... I can clearly see a Bi(n,p) after your X~. I'm not saying this is wrong, I'm just saying I don't use it cause it looks like random when you can just easily state the values.
Title: Re: Probability Notation
Post by: kamil9876 on November 08, 2009, 10:16:01 pm
It already does take on natural numbers from 5 to 10 the way he has written it. No need to specify.
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 10:18:50 pm
thats new notation to me
Will x only take whole numbers though? won't it include all the decimals in between?
Nah for summation notation, the values it takes is an element of . To be pedantic you can specify , but this is implied.

no, it already does take on natural numbers from 5 to 10 the way he has written it. You confused it with another variation that I taught you once :P
Yeah I'm not confused, I'm just saying it already takes into account for

And yeah the other notation you taught me was:

eg,
let , then

Very cool stuff.
Title: Re: Probability Notation
Post by: kamil9876 on November 08, 2009, 10:22:04 pm
or another favourite:



where d|n means n is divisible by d. (Check out Euler Totient function for more details :P)

edit: poor maths :/
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 10:37:27 pm
Or this:

Let P denote the set of all primes:



(Your other personal favorite has now become mine haha)
Title: Re: Probability Notation
Post by: ngRISING on November 08, 2009, 11:53:32 pm
or another favourite:



where d|n means n is divisible by d. (Check out Euler Totient function for more details :P)

edit: poor maths :/
Or this:

Let P denote the set of all primes:



(Your other personal favorite has now become mine haha)

what the f**K?
LOL WHAT IS THIS STUFF?
Title: Re: Probability Notation
Post by: TrueTears on November 08, 2009, 11:55:35 pm
lol kamil was giving me a lesson on summations and explained some of his favorites :P
Title: Re: Probability Notation
Post by: kamil9876 on November 09, 2009, 12:05:54 am
Yeah they actually are meaningful mathematically. But i only used them as a lesson in notation :P

Second one TT posted can be used to prove that there are infinitely many primes :)