Help completing a sample paper (1 Viewer)

[always.dreaming]

Hi there,

This morning I started working through a sample paper, can anyone please check what I have done already and also help me out with the rest of the paper?

I don’t have the answers so if anyone was kind enough to work through any of the questions to a solution that would be great thanks!

Question 7

a)
A numerical outcome of an experiment is called a random variable. If we can enumerate all possible outcomes by integers, the random variable is called discrete. If on the other hand the random variable can assume all values in some defined interval of real numbers, the random variable is called continuous.


b)

i)
10.64 (2dp)

ii)
4.82 (2dp)


iii)
…the distribution is negatively skewed.


c)

i)
15

ii)
16.26 (2 dp)

iii)

The distribution is slightly positively skewed

 

[Uncle]

What an epic maths troll.
Solving equatons using the matrix method.
It's not hard to backward substitute after performing Gaussian elimination with that matrix.

For question 3 a) i), straight forward differentiation, why can't you do it?
For question 3 a) ii), you can be a cunt and use the quotient rule, or you can treat the denominator as a term with the power of -1 and use the product rule.


For question 3 b) i), multiply the terms through expanding the brackets and you should get a polynomial with 4 terms.
For question 3 b) ii), remove the absolute value sign because it's an even function then change the limits from -1 to -1 to 0 to 1 and multiply the whole integral by 2.
You will need to do this when computing Fourier series in the future.

 

[kurt.physics]

Question 1

(a)







We must look for numbers that multiply together to give -24 and sum to give -5.

So we know we will have a negative number and a positive number because when multiplied it is the only way you can get a negative number.

The factors of 24 are 1,2,3,4,6,8,12,24.

Looking at these, -8 and 3 multiply together to give -24 and add to give -5. So we will proceed as follows








(b)










(c)













(d)



multiplying both sides by the square of the denominator





Solving yeilds



You can test inbetween each points in order to see where it is positive or consider the cubic graph of the function, in either case,

 

[kurt.physics]

Whoops, for 1 (b) I solved



instead of



The solution is as follows,











But