VCE Methods Question Thread!

[nspire]

Since time here has been limited to the measurement of seconds, would you be able to say that this is a discrete random variable because of the countable x values (in seconds)?

[Jaswinder]

Since time here has been limited to the measurement of seconds, would you be able to say that this is a discrete random variable because of the countable x values (in seconds)?

no because you can always have say 2.123982359385639486593846593845934...... seconds

[psyxwar]

How do I graph implicit functions equations on TI-Nspire CAS? (eg. y sin (3x) = x cos (3y))

[BasicAcid]

How do I graph implicit functions equations on TI-Nspire CAS? (eg. y sin (3x) = x cos (3y))

Solve for y then sketch the equation with y as the subject.

[psyxwar]

Solve for y then sketch the equation with y as the subject.

Is there any way to do it implicitly though? Some equations can't be expressed with with y as the subject.

[Phy124]

Solve for y

How do you propose to do that?

[lzxnl]

One really stupid way of doing that would be to find dy/dx implicitly, make the calculator sketch the direction field using dy/dx and then plugging in a known x,y coordinate pair (such as subbing in x = 0 or y = 0; whatever simplifies things). The calculator should draw a curve that corresponds to what you want.

Although admittedly, this is pretty stupid. And of course, it'll make no sense if you haven't seen any bits of spesh before.

For a special class of functions that exist in parametric form, you'll be able to use the parametric function ability.

[psyxwar]

One really stupid way of doing that would be to find dy/dx implicitly, make the calculator sketch the direction field using dy/dx and then plugging in a known x,y coordinate pair (such as subbing in x = 0 or y = 0; whatever simplifies things). The calculator should draw a curve that corresponds to what you want.

Although admittedly, this is pretty stupid. And of course, it'll make no sense if you haven't seen any bits of spesh before.

For a special class of functions that exist in parametric form, you'll be able to use the parametric function ability.

Thanks, seems like a lot of effort. Ah well, I was just asking because I wanted to try plotting weird shapes on the CAS.

Well I've never used a TInspire before so I was assuming as it's a calculator which is supposed to be equivalent to the CAS one I use which cost me a lot of money.
And for $150+ you'd expect it to be able to solve/rearrange relatively simple equations.

So sorry, I didn't know the TInspire couldn't solve basic equations for a specific subject.

Nah, he's saying that you can't express the example I gave in terms of y (try using your classpad or whatever, it doesn't work).

[lzxnl]

Well I've never used a TInspire before so I was assuming as it's a calculator which is supposed to be equivalent to the CAS one I use which cost me a lot of money.
And for $150+ you'd expect it to be able to solve/rearrange relatively simple equations.

So sorry, I didn't know the TInspire couldn't solve basic equations for a specific subject.

The equation that was given wasn't basic. The TI-Nspire would be able to let you sketch x^2+sin^2(2y) = 1, for instance. Unfortunately it doesn't have an implicit equation sketching facility.

[nspire]

no because you can always have say 2.123982359385639486593846593845934...... seconds

Thanks!!

[b^3]

How do I graph implicit functions equations on TI-Nspire CAS? (eg. y sin (3x) = x cos (3y))

You can plot implicit functions on the Ti-nspire, it just takes a long time to do it sometimes.
Try rearranging the equation so that it is equal to zero, then in the graph bar type 'zeros(. It will take a while to graph it in this case, for simpler functions it will do it in less time (I think in this case it's more the fact that you have two trig functions).

It may help for future reference for other curves though. E.g. Try plotting using that method.

...Although now that I think about it the updated OS has a template for ellipses and such. But anyways, it may or may not come in handy (this was our little trick before that update came in. I don't have the new calc on me atm to test/check what you guys have).

It's not giving the exact plot that wolfram gives (damn). There is a way to do it but I can't seem to remember/work it out currently.

[Sanguinne]

i have no clue how to solve the following questiom, help is appreciated

Phil is running a stall at the local Primary School Fair involving lucky dips. It costs $2 to have a go, and contained in a large box are 80 lucky dips from which to choose. Phil claims that one in 5 lucky dips contains a prize. By the end of the day, all 80 have been sold. Calculate the probability, correct to 4 decimal places that:
a) the first four people to select a lucky dip don't win a prize, but the next two do
b) there are at least 10 winners
c) there are no more than 18 prize winners, given that at least 10 people won a prize.

[Jaswinder]

a)(4/5)^4*(1/5)^2
b) binomialCDF (10,80,80,1/5)
c) binomialCDF(0,18,80,1/5) divided by binomial CDF(10,18,80,1/5)

[BasicAcid]

i have no clue how to solve the following questiom, help is appreciated

Phil is running a stall at the local Primary School Fair involving lucky dips. It costs $2 to have a go, and contained in a large box are 80 lucky dips from which to choose. Phil claims that one in 5 lucky dips contains a prize. By the end of the day, all 80 have been sold. Calculate the probability, correct to 4 decimal places that:
a) the first four people to select a lucky dip don't win a prize, but the next two do
b) there are at least 10 winners
c) there are no more than 18 prize winners, given that at least 10 people won a prize.

Always state given conditions:

The $2 is irrevelant in this question.
"One in 5 lucky dips contains a prize" -> p = 1/5 = 0.2
"80 lucky dips from which to choose" -> n = 80


a) You can draw a tree diagram or you can just work it out.
0.8^4 * 0.2^2 = 0.0164



b) "At least 10 winners" i.e. Pr (X greater than or equal to 10)
Use BinomialCDf on CAS:
Lower: 10
Upper: 80
Numtrial: 80
pos: 0.2

= 0.9713



c) "there are no more than 18 prize winners, given that at least 10 people won a prize."
i.e. Pr (X less than or equal to 18 | X greater than or equal to 10)
Pull out your formula sheet:
Intersection between the two conditions above divided by your answer in part b.

Intersection between less than or equal to 18 and greater than or equal to 10 is Pr([10,18]).
i.e. BinomialCDf once again:
Lower: 10
Upper: 18
Numtrial: 80
pos: 0.2

= 0.7333623149

Note: When using previous answer, get as many decimal places as you can so there are no rounding errors.

--> 0.7333623149/0.9712824327 = 0.7550

[darklight]

Hi guys,

Another question from ATARNotes Q6; Probability Tech-Active Test 2. The function given is k^2 * (cos(x) +1)) from pi to 0. In order for it to be a p.d.f f(x) needs to be greater than or equal to 0 right? So why can't k be negative? Because won't the square remove the negative, satisfying all conditions?