VCE Methods Question Thread!

[Sayf44]

If your transition matrix is:
           A    B
A    [  0.3   0.5   ]
B    [  0.7   0.5   ]

The long term Pr(A) =  0.5 / (0.5 + 0.7)
The long term Pr(B) =  0.7 / (0.5 + 0.7)

EDIT: The reason why its like that is because were interested in the probability of changing from, for ex, B to A, divided by the sum of the two probabilities that result in a change (0.5 + 0.7 in this case - its ok if this number is greater than 1). That will tell us the exact long term probability of sticking with A. Or vice versa for A to B.

I use this method too although tbh I don't understand it.. I just know how to do it. How would you show the working out using this method though? I mean I don't think 0.5/(0.5+0.7) is enough for 2-3 marks.

[Blondie21]

Just write y=2x in every page that's blank hahahahaha

LMAOO

btw why aren't we allowed to write in our bound ref?

[Reus]

What does "calculate Pr(A' ^ B) when A and B are mutually exclusive events" even mean .____.

[faredcarsking123]

For Q19 in 2013 VCAA Exam 2, in the solution it says solve in the domain [0, 3pi]

Where did they get this domain from?



Also can someone explain VCAA Exam 2 2007 quesiton 5fii please?

Thank you
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[psyxwar]

What does "calculate Pr(A' ^ B) when A and B are mutually exclusive events" even mean .____.

Mutually exclusive = nothing in common, eg. a venn diagram with no intersection between A and B (so two separate circles).

Everything outside of A intersection B for mutually exclusive A and B is thus just the Pr(B). Try drawing out a diagram.

[Jason12]

Do I define g(x) and just sub in to all the options? I tried it and none say true in the nspire cas

[GeniDoi]

(Image removed from quote.)

Do I define g(x) and just sub in to all the options? I tried it and none say true in the nspire cas

2g(8x) = 2*Log2(8x) =  Log2((8x)^2) = Log2(64 * x^2) = Log2(x^2) + Log2(64)  = Log2(x^2) + 6

Therefore B.

[Robert123]

For Q19 in 2013 VCAA Exam 2, in the solution it says solve in the domain [0, 3pi]

Where did they get this domain from?



Also can someone explain VCAA Exam 2 2007 quesiton 5fii please?

Thank you
Modify message

Look at the x intercepts. The intercepts are 0. Pi. 2pi and 3pi. Looking at the graph, you can see that T3 lies between 2pi and 3pi, and that's your domain

(Image removed from quote.)

Do I define g(x) and just sub in to all the options? I tried it and none say true in the nspire cas

Since all the options have the same left hand side, I would play around with that first and see what you can make it look like. This question does require the use of multiple log laws and make sure to take into account that it's log2 not loge.
Do you want any more hints?

[Blondie21]

lmao I just drew up the graphs on the CAS :3 (in re: to Jason21's q)

[paper-back]

For Q19 in 2013 VCAA Exam 2, in the solution it says solve in the domain [0, 3pi]

Where did they get this domain from?



Also can someone explain VCAA Exam 2 2007 quesiton 5fii please?

Thank you
Modify message

VCAA Exam 2 2007, Question 5fii)
We know that the probability is
and that;

Therefore,

and

[GeniDoi]

I use this method too although tbh I don't understand it.. I just know how to do it. How would you show the working out using this method though? I mean I don't think 0.5/(0.5+0.7) is enough for 2-3 marks.

This would never be a 3 mark question and for 2 marks its sufficient. If its a 3 mark question they would have to be asking for both steady state probabilities, in which you just to  Pr(B) = 1 - Pr(A) when you figured out Pr(A) or otherwise using the steady state formula twice.

           A      B
A    [    p    1-n  ]
B    [  1-p    n    ]


Theres several ways to think about it, but its methods and methods doesn't require you to understand the deep intrinsic parts of the mathematics, rather just know how to use them. Think of it this way, theres a certain chance A changes to B, and 1 - (that chance) is the chance B changes to A. As your approach an infinite amount of changes, the probability of being A or B will be the probability of sticking with A or B during a change, divided by the sum of the two probabilities involving a change. The trend will be


The long term Pr(A) =  1-n / (1-n + 1 - p)
The long term Pr(B) =  1-p / (1-n + 1 - p)

[Professor_Oak]

Do we have to include a scale for our sketch graphs if one is not provided?

[jonoz0r]

Do we have to include a scale for our sketch graphs if one is not provided?

Anyone correct me if I'm wrong, but I think 'realistic scaling' is required for sketch graphs (i.e. x=1 cannot be right next to x=10), but if grid paper is provided, then you MUST provide proper scaling

[faredcarsking123]

Look at the x intercepts. The intercepts are 0. Pi. 2pi and 3pi. Looking at the graph, you can see that T3 lies between 2pi and 3pi, and that's your domain.

THANKS ROBERT

VCAA Exam 2 2007, Question 5fii)
We know that the probability is
and that;

Therefore,

and

Thank you that made me understand it much better, my last question is how do we know that b in between 20 and 30 and not 10 and 20?

[Professor_Oak]

Anyone correct me if I'm wrong, but I think 'realistic scaling' is required for sketch graphs (i.e. x=1 cannot be right next to x=10), but if grid paper is provided, then you MUST provide proper scaling

I was more talking about labeling a scale if one is not provided.