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# Need help with C4 and S2 watch

1. Asking alot here so I'd appreciate any help. Once again I'm failing at maths and I'm struggling to even get started on some of these questions.

S2

6) The continuous random variable X has p.d.f given by:

f(x) = {1/4x^3, 0 < x < 2 (less than or equal to / greater than or equal to signs)
{0, otherwise.

a) Sketch the p.d.f of X. (*shrug*)
b) Write down the mode of X. (I thought you had to differentiate f(x), make it equal to 0 and solve for X but I can't get a straight answer and the back of the book says that the answer is 2 )

C4

1) l1 has a vector equation r = (11,5,6) + ?(4,2,4), where ? is a parameter
l2 has a vector equation r = (24,4,13) + ?(7,1,5), where ? is a parameter.

a) Show the lines l1 and l2 intersect
b) Find the co-ordinates of their point of intersectiion

Given that ? is the acute angle between l1 and l2
c) Find the value of cos ?. Give your answer in the form k?3, where k is a simplified fraction.

---

Thanks in advance again. With C4, I know the basics of finding the point of intersection but there's alot of vectors so I'm getting confused.

2. (Original post by Wolfiexe)
Asking alot here so I'd appreciate any help. Once again I'm failing at maths and I'm struggling to even get started on some of these questions.

S2

6) The continuous random variable X has p.d.f given by:

f(x) = {1/4x^3, 0 < x < 2 (less than or equal to / greater than or equal to signs)
{0, otherwise.

a) Sketch the p.d.f of X. (*shrug*)
b) Write down the mode of X. (I thought you had to differentiate f(x), make it equal to 0 and solve for X but I can't get a straight answer and the back of the book says that the answer is 2 )

C4

1) l1 has a vector equation r = (11,5,6) + ?(4,2,4), where ? is a parameter
l2 has a vector equation r = (24,4,13) + ?(7,1,5), where ? is a parameter.

a) Show the lines l1 and l2 intersect
b) Find the co-ordinates of their point of intersectiion

Given that ? is the acute angle between l1 and l2
c) Find the value of cos ?. Give your answer in the form k?3, where k is a simplified fraction.

---

Thanks in advance again. With C4, I know the basics of finding the point of intersection but there's alot of vectors so I'm getting confused.

For S2 is it (x^3)/4 or 4x^-3?

for the C4 Vectors, you can re-write the x and y positions down, make them equal to eachother and solve the simultaneously.
I will let your ? for l1 = x and ? = y for l2, this gives
11+4x = 24+7y
5+2x = 4+y
Solve them and find values for x and y, then check this for the z values by subbing in your known values of x and y into the equation for z, which is 6+4x=13+5y, they they are equal to eachother, they intersect, if they aren't then the lines are skew.
To find the co-ordinates of the point of intersection, sub in your known values of x into the vector line equation, then add them and this will give you the position vector of the intersection point, to make sure, I would then sub in the y value into the l2 to make sure you get the same vector as l1.

For the angle, you need to learn the scalar product equation,
Not really much else to say about that without actually doing it for you, you can work out the values of A and B using 3D pythagoras, and also work out ab by adding up each term of the vector found when the values are multiplied by the corresponding values in each vector
eg where the letters are constants, gives the value ax + by + cz
3. I was told that 4x^-3 cannot be a p.d.f by Get me off the £\?%!^@ computer, thanks for that
You should know how to draw the graph of x^3, and from C1 graph sketching, you should be able to draw it. I will get back to you on the rest unless someone beats me to it, I have a lesson now
I was told that 4x^-3 cannot be a p.d.f by Get me off the £\?%!^@ computer, thanks for that
You should know how to draw the graph of x^3, and from C1 graph sketching, you should be able to draw it. I will get back to you on the rest unless someone beats me to it, I have a lesson now
5. (Original post by Wolfiexe)
S2

6) The continuous random variable X has p.d.f given by:

f(x) = {1/4x^3, 0 < x < 2 (less than or equal to / greater than or equal to signs)
{0, otherwise.

a) Sketch the p.d.f of X. (*shrug*)
b) Write down the mode of X. (I thought you had to differentiate f(x), make it equal to 0 and solve for X but I can't get a straight answer and the back of the book says that the answer is 2 )
b)The mode is the one which occurs the most frequent. I think part a) comes in handy here, what you done by differentiating is finding the stationary point, which may work in some cases, but I think you'll find it doesn't help in this case. What if you had a U shaped curve, the stationary point will give you the least frequent value!). So once you have differentiated, the highest value of x is 2(because the area of the p.d.f has to equal 1, so the limits are 0 and 2).

As I said, my explanation isn't the best, it relies on an accurate sketch, you'll see the highest point is at x=2

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