VCE Methods Question Thread!

[generalkorn12]

Could anyone tell me how to interpret this question, the worked solution is really vague.

[BubbleWrapMan]

Try drawing a Venn diagram?

[Lasercookie]

We have events P and Q.
We know that this statement is true.

We want them to be independent events. In other words we want: (the event Q has no effect on event P). Anyway, if they're independent then this means .

From a Venn diagram, we can see that

Given that , this means that

Solve for Pr(P), we get

[TrueTears]

Just providing another perspective:

P(P)P(Q) = P(P')P(Q) [Since if P is independent with Q then P' is independent with Q, very easy to prove. In fact if P is a RV, then any function of P, say g(P) is also independent with Q, and if we assume Q is also a RV, then g(P) and h(Q) are also independent for any functions g and h, independence is a very powerful result ]

Assuming P(Q) > 0

P(P) = P(P')

P(P') = 1-P(P)

P(P) - (1-P(P)) = 0

P(P) = 1/2

[soccerboi]

When i type nCr(5,3) on CAS, it gives me 10. But isn't that equal to (5x4x3x2x1)/(3x2x1)=20???

I'm forgetting something aren't i?

[Lasercookie]

When i type nCr(5,3) on CAS, it gives me 10. But isn't that equal to (5x4x3x2x1)/(3x2x1)=20???

I'm forgetting something aren't i?

[generalkorn12]

Thanks for that Lassered and TrueTears!! I appreciate getting different perspectives on approaching a question. 

I've just got one more problem involving General Solutions;

For the question attached, I'm having trouble understanding where that formula could be derived from...

[TrueTears]

HOW TO: Solve for general solutions for circular functions

[aishuwa1995]

Hi, can someone please tell me how to do this question? 
tech-free

[TrueTears]

h'(x) = (n/x-1)x^ne^{-x}

stationary point when x = n.

h''(n) < 0 since n is a positive integer

so local max

[aishuwa1995]

h'(x) = (n/x-1)x^ne^{-x}

stationary point when x = n.

h''(n) < 0 since n is a positive integer

so local max

I don't understand how the quotient rule can give that h'(x)? (I get that when I use my CAS but it's an exam 1 question)

[TrueTears]

h(x) = x^n e^{-x}

h'(x) = nx^{n-1} e^{-x} - x^n e^{-x} = x^ne^{-x} (nx^{-1} -1)

[Lasercookie]

If you wanted to use the quotient rule, you can still get the same answer that TT got out using the product rule like this:

[aishuwa1995]

got it  thanks TrueTears and laseredd

[Bhootnike]

Got stuck with this:

integrate sin^2(x) using integration by parts

can someone please help ?!