VCE Methods Question Thread!

[melons]

Help on part c please....

[polar1]

Help on part c please....

Fun question!

Let be the volume of a standard bottle and the volume of a large bottle. Then, what you want is basically . So, you have

A more intuitive approach here

So, put yourself in the situation. You might choose four standard bottles, add up their volumes, let's call that . Then, you'd choose three large bottles, and add up their volumes. Let's call that . Now, what you want is , or, . Now, all we need is .

But, and are identically distributed, same with and . So, call these distributions S and L, and you have

Let's call the difference . Then, it's just a matter of finding .

Because and are normally distributed, is as well. We should find the expected value and standard deviation of D.

Using the facts given in the question, we have and, .

So, we have

Chuck that into your calculator or standardise and use a table, and you get an answer of 0.59439.

[melons]

Fun question!

Thank you!

[Brunette15]

If you were asked to find the sample space of two dice being rolled do you have to repeat certain combinations. For example if you have already listed that a possible combination is a 1 and a 3. Would you also have to include that a possible combination is a 3 and a 1? The dice are being rolled simultaneously.

[keltingmeith]

If you were asked to find the sample space of two dice being rolled do you have to repeat certain combinations. For example if you have already listed that a possible combination is a 1 and a 3. Would you also have to include that a possible combination is a 3 and a 1? The dice are being rolled simultaneously.

It depends on the wording, but in general, I would say yes. Let's say your sample space is the set of ordered pairs (x, y), then x would refer to the outcome of the first die, and y would refer to the outcome of the second. If you say that (1, 3) is a possible outcome, but (3, 1) isn't, you're saying that while the first die can be 1 if the second die is 3, the first die cannot be 3 while the second die is 1, and we know that the second statement isn't true, as both events are independent of each other.

[Jason12]

in a probability distribution function, does the area always = 1? If so, how do i use it to figure this out?

[keltingmeith]

Yes - the area under the curve must ALWAYS be equal to 1. This goes back to the definitions of probability you initially learned, in that the sum of all possible probabilities should equal 1.

So, in this case, we know that the area under the curve is given by , and that this should equal 1. So, we have:

[knightrider]

How would you do these questions

Use first principles to find   

[IndefatigableLover]

How would you do these questions

Use first principles to find   

I'll do one of them and then you can do the other one to check

So with a), say we let y= f(x), then we can then find f(x+h)



Now we need to find which can be found using:



Sub in the values:









Now use the same technique for the second question

[keltingmeith]

Is sketching:

f(x)=(x-1)^2/3 +2

possible tech-free?

I mean I just saw it on a MAV exam 1 but I have never been taught in class how to sketch it. Dare I ask, is it part of the course?

Depends - are you talking about or ?

If it's the first, it's just a normal parabola. If it's the second, I'd have to double check the study design, but it might not be. Granted, the second isn't that hard to draw - just logic it. is just like the second one - so, just draw the normal cube root graph, square every value, and then move it up 2.

[IndefatigableLover]

Depends - are you talking about or ?

If it's the first, it's just a normal parabola. If it's the second, I'd have to double check the study design, but it might not be. Granted, the second isn't that hard to draw - just logic it. is just like the second one - so, just draw the normal cube root graph, square every value, and then move it up 2.

With the second equation, I'm pretty sure you need to know how each 'power function' looks like (that is if the numerator/denominator is even/odd and if it's between 0 & 1).. it's in Essentials somewhere (can't remember where) and also appears in a few revision guides I've read such as Alwin's SAC 2 (provided that each school does their SAC's differently but I'm sure Alwin knows what he's talking about when it comes to Maths LOL)

[keltingmeith]

How do you solve for x?
 
-ln(1-x)-1=(e^-x) -1

Techfree. PS: They're inverses of each other, if that helps at all...

It's a MAV trial exam question and the answer is (0,0). But I can't do it by hand??

Is the actual question ", solve for x", or is it something else and you're interpreting it this way? Because x=0 isn't a solution to this equation.

[kinslayer]

How do you solve for x?
 
-ln(1-x)-1=(e^-x) -1

Techfree. PS: They're inverses of each other, if that helps at all...

It's a MAV trial exam question and the answer is (0,0). But I can't do it by hand??

You've made a typo or something, those two functions aren't inverses (and don't intersect at (0,0)).

For this type of question, try graphing the function then graphing y=x alongside it. Any intersection points will also be intersection points with the function and its inverse, if it has one. For example if y = e^(-x) - 1 then it will intersect its inverse at (0,0) because it goes through the origin.

[Brunette15]

It depends on the wording, but in general, I would say yes. Let's say your sample space is the set of ordered pairs (x, y), then x would refer to the outcome of the first die, and y would refer to the outcome of the second. If you say that (1, 3) is a possible outcome, but (3, 1) isn't, you're saying that while the first die can be 1 if the second die is 3, the first die cannot be 3 while the second die is 1, and we know that the second statement isn't true, as both events are independent of each other.

Thankyou! 

[jessss0407]

The wording of the first question is far beyond what I would expect of a methods students (pretty sure a few of the people in my second year stats class don't know what half of those words mean...). However, it is just the normal rule to find the z-score - if and , then

The second one is a little annoying, and while I wouldn't expect to see it on an exam, it is definitely still in the realm of things you could be asked and what your school might ask.

So, we know that all distributions are symmetrical about the mean. So, if we can find the point where one side is equal to 0.45, we can find one point. We also know that the standard normal is symmetrical about the mean, so each of the values will be the same number, but one will be negative and one will be positive. So, if we can find the answer for the standard normal, we can then convert to the particular distribution we have now. (from this paragraph onwards, you might find it beneficial to draw a bunch of normal distributions and shade in the areas we're trying to find)

So, we define , and then try to find . Now, cutting this in half, what we want to find is . Now, the final step is to turn this around - find the probability that Z is LESS than -d. When we do this, we're looking for 0.5-0.45=0.05 instead. This works in our favour, because now we can use the inverse normal function on our calculator. So, we find . Now, finally we just need to apply some transformations to get to the give normal distribution. So, . Now, remember we need to do this for both a positive d and a negative d. The lower value will be c1, the upper value will be c2. This gives us

Wow, thanks! one question tho, how do you know that Pr (-d<Z<0) is definitely 0.45 on the standard normal? is there a possibility that Pr(-d<Z<0) could be 0.3 and Pr(d>Z>0)is 0.6 or something like that?

Thanks