VCE Methods Question Thread!

[keltingmeith]

I need help finding the constant k (attached)

What information have you been given? How can you use this information?

[Floatzel98]

What information have you been given? How can you use this information?

oh yeah, kind of didn't add anything else. It is a probability density function. I tried going something like this:

since for



But I really don't know what to do after that (or if that approach is even correct). I tried putting the same thing in my calculator but didn't come back with the answer. I just started continuous probability and just basing my method on the example from the book, but it doesn't seem to be working.

[cosine]

Sometimes, you can think of probabilities as a proportion. For example, if a particular coin has a probability 0.666 of getting a heads, then over a long period of time, we expect to see 66.6% of our coins come up as heads.

Sorry Euler what exactly do you mean?

[keltingmeith]

oh yeah, kind of didn't add anything else. It is a probability density function. I tried going something like this:

since for



But I really don't know what to do after that (or if that approach is even correct). I tried putting the same thing in my calculator but didn't come back with the answer. I just started continuous probability and just basing my method on the example from the book, but it doesn't seem to be working.

Okay, so if k is in the function, don't use k for the variable. Otherwise, you're on the right track. Try antidifferentiating and go from there, you're very close.

[keltingmeith]

Sorry Euler what exactly do you mean?

So basically, to find this long term proportion, you need to find a long term probability. What happens to a Markov Chain over a long period of time?

[Floatzel98]

Okay, so if k is in the function, don't use k for the variable. Otherwise, you're on the right track. Try antidifferentiating and go from there, you're very close.

Oh yeah. That makes so much more sense haha. The examples all used k as the limit variable so I automatically did that too. Thanks Euler.

[cosine]

Why do we have to use the discriminant? I thought the discriminant was only used for the amount of x-intercepts, but this example is talking about intersections?

[shivaji]

Why do we have to use the discriminant? I thought the discriminant was only used for the amount of x-intercepts, but this example is talking about intersections?

You use discriminant for number of SOLUTIONS. So it doesn't matter whether x-ints or intersections points, the discriminant needs to be satisfied.

[cosine]

For the question attached, I got the same answer but had it in fraction, VCAA 2008 exam 1, would full marks be given If i showed all working out and included my answer in fraction? (They don't say whether to use decimal or fraction)

Many thanks guys

[Maca 13]

Hey everyone!
I was wondering if anyone could please help me answer part c) to this question? Its all part of the same question.
I understand how to do the other 2 parts but not the last one?

Spoiler

The answer to c) is 2/5

Thanks, I really appreciate it!
EDIT: I figured out how to do it.

[Floatzel98]

I've been stuck on this question for a while. How do I solve this:



I know I have to put this in the calculator but I'm not really sure what to do / how to get rid of the binomial coefficient.

[Adiamond]

Hey man the calculator can just do it all, i'm gonna assume you have the same calc as me for this (Ti-nspire cx), if you go to the menu  there should be a subheading called probability which contains a few different helpful things for probability, in here should be a 'combinations' button which comes up as 'nCr()'. What you want to put in here is the top number, a comma, and then the bottom number. e.g. the binomial coefficient for your question would be nCr(n,5).
Knowing this we can just insert the equation into our calculator and solve for n.
solve(nCr(n,5).(0.6)^5.(0.4)^n-5=0.25,n) and you should get either 6.7856 or 9.01913

(disclaimer: this may be completely wrong but that's how I would solve that question, maybe we should wait for someone like eulerfan101 to come and show us both how to do it)

Edit: I found a similar question in the essentials textbook Ch 15D question 3 which asks for the minimum number of shots required for the probability to be greater than 25%, meaning that you would take the smallest integer possible from the calculator answers which would be 7 shots (even if the answer was 6.000000001 it would still need to be 7 shots).

[Floatzel98]

Hey man the calculator can just do it all, i'm gonna assume you have the same calc as me for this (Ti-nspire cx), if you go to the menu  there should be a subheading called probability which contains a few different helpful things for probability, in here should be a 'combinations' button which comes up as 'nCr()'. What you want to put in here is the top number, a comma, and then the bottom number. e.g. the binomial coefficient for your question would be nCr(n,5).
Knowing this we can just insert the equation into our calculator and solve for n.
solve(nCr(n,5).(0.6)^5.(0.4)^n-5=0.25,n) and you should get either 6.7856 or 9.01913

(disclaimer: this may be completely wrong but that's how I would solve that question, maybe we should wait for someone like eulerfan01 to come and show us both how to do it)

Thanks for the help. I have actually been doing that and it isn't working. Granted I have the Classpad, not the Ti-nspire. It just comes up with the binomial coefficient expanded with the factorials. It won't actually solve it. 

Yeah, it actually is that question. I know the method but my calculator just won't do it.

[cosine]

For the question attached, I got the same answer but had it in fraction, VCAA 2008 exam 1, would full marks be given If i showed all working out and included my answer in fraction? (They don't say whether to use decimal or fraction)

Many thanks guys

Anyone please?

[HopefulLawStudent]

The question is asking for average cost through so you can't simply find the minimum of the function stated in the question. You will need to find an equation that describes the average cost of a unit and then find the minimum of that. I would also round off to the nearest integer at the end.

Thank you for taking the time to explain.

I have done probability which is why the mention of the continuous stuff threw me off because it was supposed to be a purely calculus revision exercise so I worried there'd be some probability (*shudder*) trick to the question.

What do you mean when you say I have to find an average cost equation? Why can't I use the cost equation given in the question for my calculations?