VCE Methods Question Thread!

[GloriousHeights]

Hi  Can someone please help me with VCAA 2015 exam 2, question 2a, how to find the angle?

[DailyInsanity]

Hi guys,

Does a hybrid probability density function have to be continuous? Not at the end points where it may drop to 0 but in the transfer from one function in the hybrid to the other - i.e) does the y co-ordinate have to be the same when one function ends and the other starts? Thanks in advance!

[LifeisaConstantStruggle]

Hi guys,

Does a hybrid probability density function have to be continuous? Not at the end points where it may drop to 0 but in the transfer from one function in the hybrid to the other - i.e) does the y co-ordinate have to be the same when one function ends and the other starts? Thanks in advance!

from my understanding, no, it does not have to be continuous, since the end points where it drops to 0 and where it goes are technically still functions of a graph (y=0), but be aware of the open or closed endpoints of the function because that might be used to trick people.

[LifeisaConstantStruggle]

Hi  Can someone please help me with VCAA 2015 exam 2, question 2a, how to find the angle?

Note that tan(theta)=gradient of the point on the function so you can solve it from there (with your CAS of course).

[thesplaaashman]

Exam 1 Questions

The question wants the probability that a box is labelled incorrectly. The box will be labelled incorrectly when it is a Grade A and it has a use-time of less than 10.5 hours (intersection of probabilities), or it is Grade B and has a use-time of more than 10.5 hours.
Please post if you're still stuck :)
Hope this helps! :)
[/quote

Thanks:). I'm stll a bit confused though. I understand that you need to draw a tree diagram, but why is the box considered as labelled incorrectly when it has a use-time less than 10.5 hours and vice versa? Couldn't it have been labelled incorrectly if it has a use-time of greater than 10.5 minutes? Probably a stupid question but I don't see it for some reason.

[LifeisaConstantStruggle]

Thanks:). I'm stll a bit confused though. I understand that you need to draw a tree diagram, but why is the box considered as labelled incorrectly when it has a use-time less than 10.5 hours and vice versa? Couldn't it have been labelled incorrectly if it has a use-time of greater than 10.5 minutes? Probably a stupid question but I don't see it for some reason.

Drawing a tree diagram would probably leave you with 4 different outcomes, and 2 of it will be a mistake (where the boxes are labelled incorrectly), so you have to identify the 2 outcomes that would result in the incorrect labeling of boxes. Hope that helps.

[Rieko Ioane]

Hey this question is kinda flawed in wording but they are looking for the total number of calls (2,2) and because 2M2T is the same order as 2M2T they don't count it as different variables (or accounts yknow what I mean). 1M3T and 3M1T would be considered different due to the day (this is kinda self explanatory).

Thanks.

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Also, does anyone know if we need to use units in our answers?

VCAA 2014 Q4 ER seems to care about units but doesn't say if students lose marks without using them.

[usernameincorrect]

Hello!

For composite functions of f(g(x)), is it true that the range of g(x) is equal to, or a subset of the domain of f(x)? Cheers!

[LifeisaConstantStruggle]

Hello!

For composite functions of f(g(x)), is it true that the range of g(x) is equal to, or a subset of the domain of f(x)? Cheers!

nope.
A composite function only exists if the range of g(x) is a subset of the domain of f(x), if this is true, then the domain of the composite function f(g(x)) would be the domain of g(x).
If not, you would have to change the range of g(x) so that it fits within the domain of f(x), and with that, you have to change the domain of g(x) so that it fits its own range, and the changed domain will be the domain of your composite function.
Hope that helps.

[LifeisaConstantStruggle]

Thanks.

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Also, does anyone know if we need to use units in our answers?

VCAA 2014 Q4 ER seems to care about units but doesn't say if students lose marks without using them.

Hey, although its not an explicit requirement (unless if its conversion from hours to minutes or things like that) it would probably be safer to include units, just in case. (sometimes I would write units² if I do the area under a graph questions, just in case)

[zxcvbnm18]

Hey, can the expected value (mean) of a probability distribution table be negative?

[Eric11267]

Hey, can the expected value (mean) of a probability distribution table be negative?

Yes it can, only the probabilities themselves can't be negative

[LifeisaConstantStruggle]

Yes it can, only the probabilities themselves can't be negative

Standard deviations cannot be negative too.
All STDs are positive.

[uhoh]

I don't understand c) ii from the 2013 methods exam 
I know that you find Pr(x>4) and multiply by 200
but the question says "...expected..."- doesn't this mean that we need to find E(x)? So we use E(x)=np= 200*Pr(x>4) (getting the same ans as the line above). Even though we get the same ans, the question isn't binomial though, so maybe we can't use E(x)=np?

[VanillaRice]

I don't understand c) ii from the 2013 methods exam 
I know that you find Pr(x>4) and multiply by 200
but the question says "...expected..."- doesn't this mean that we need to find E(x)? So we use E(x)=np= 200*Pr(x>4) (getting the same ans as the line above). Even though we get the same ans, the question isn't binomial though, so maybe we can't use E(x)=np?

It sort of is binomial - we have a defined number of trials (200), and the probability remains constant for every trial (i.e. everyone has the same probability of taking more than 4 minutes).
Either way - you don't need to think of it as binomial. Let's say (for example) that we know that 1/5 of Australians are male. If I have you a sample of 5 random Australians, how many would you expect to be male? 1 - since the probability is 0.2, and we multiply by 5 to get 1.

Hope this helps