Exam (elaborations)

Mock exam + worked solutions for chapters 6&7 (AS statistics)

0 purchase

Course
Mathematics

Institution
University College London (UCL)

A document featuring exam questions and worked solutions for A-level Maths is invaluable. It offers vital practice opportunities, enhances understanding through step-by-step explanations, aids in error identification and correction, familiarizes students with exam formats, comprehensively covers sy...

[Show more]

Preview 3 out of 18 pages

View example

Uploaded on March 19, 2024
Number of pages 18
Written in 2023/2024
Type Exam (elaborations)
Contains Questions & answers

mock exam
exam paper
a level maths
statistics
binomial distribution
hypothesis testing

Institution
University College London (UCL)
Education Unknown
Course
Mathematics

$7.77

Add to cart

Add to wishlist

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

YEAR 12 MATHEMATICS
- Chapters 1&2-
6&7 Statistcs-

(45 Minutes)

NAME: __________________
Worked Solutions TEACHER: _______________
SCK -

MARKS: ____
45 /453
43
.

Candidates may use any calculator allowed by the regulations of the
Joint Council for Qualifications. Calculators must not have the facility
for symbolic algebra manipulation, differentiation and integration, or
have retrievable mathematical formulae stored in them.
Instructions
● Use black ink or a ball-point pen.
● If pencil is used for diagrams / sketches / graphs it must be dark (HB or B).
● Fill in the boxes at the top of this page with your name,
centre number and candidate number.
● Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
● Answer the questions in the spaces provided
– there may be more space than you need.
● You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
● Answers should be given to three significant figures unless otherwise stated.
Information
● A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
43
● There are 7 questions in this question paper. The total mark for this paper is e
45.
● The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
● Read each question carefully before you start to answer it.
● Try to answer every question.
● Check your answers if you have time at the end.

, Statistics
Discrete distributions

For a discrete random variable X taking values xi with probabilities P(X = xi )
Expectation (mean): E(X ) = μ = Σxi P(X = xi )
Variance: Var(X ) = σ 2 = Σ(xi – μ)2 P(X = xi ) = Σ x2i P(X = xi ) – μ 2
For a function g(X ): E(g(X )) = Σg(xi ) P(X = xi )
The probability generating function of X is GX (t) = E(t X ) and
E(X ) = G′X (1) and Var(X ) = G′′X (1) + G′X (1) – [G′X (1)]2
For Z = X + Y, where X and Y are independent: GZ (t) = GX (t) × GY (t)

Discrete distributions

Standard discrete distributions:

Distribution of X P(X = x) Mean Variance P.G.F.

 n x
 x p (1 – p)
n –x
Binomial B(n, p) np np(1 – p) (1 – p + pt)n

λx
Poisson Po(λ) e− λ λ λ eλ(t –1)
x!

Geometric Geo( p) 1 1− p pt
p(1 – p)x –1
on 1, 2, . . . p p2 1 − (1 − p )t

r
Negative binomial  x − 1 r r r (1 − p )  pt 
 r − 1 p (1 – p)
x –r
on r, r + 1, . . . p p2  1 − (1 − p )t 

4
Continuous distributions

For a continuous random variable X having probability density function f

Expectation (mean): E(X ) = μ = ∫ x f(x) dx

Variance: Var(X ) = σ 2 = ∫ (x – μ)2 f(x) dx = ∫ x2 f(x) dx – μ 2

For a function g(X ): E(g(X )) = ∫ g(x) f(x) dx
x0
Cumulative distribution function: F(x0) = P(X  x0 ) = #
−∞
f (t) dt

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics 23

, Standard continuous distribution:

Distribution of X P.D.F. Mean Variance

2
1 x − μ
1 −  
Normal N(μ, σ 2) e 2 σ 
μ σ2
σ 2π

1 1
Uniform (Rectangular) on [a, b] 1
(a + b) (b – a)2
b−a 2 12

Correlation and regression

For a set of n pairs of values (xi , yi )

(Σ xi ) 2
Sxx = Σ(xi – x)2 = Σxi2 –
n
(Σ y i ) 2
Syy = Σ( yi – y)2 = Σyi2 –
n
(Σ xi )(Σ y i )
Sxy = Σ(xi – x)( yi – y) = Σxi yi –
n

The product moment correlation coefficient is

(Σ xi )(Σ y i )
Sxy Σ xi y i −
Σ( xi − x )( y i − y ) n
r = = =
SxxS yy {Σ( x − x )2 }{Σ( y − y )2 }  2 (Σ xi )   2 (Σ y i ) 2 
2

 Σ xi − n   Σ y i − n 
i i

Sxy Σ( xi − x )( y i − y )
The regression coefficient of y on x is b = =
Sxx Σ( xi − x ) 2

Least squares regression line of y on x is y = a + bx where a = y – bx

(S )
2
xy
Residual Sum of Squares (RSS) = Syy – = Syy (1 – r 2)
Sxx

6Σd 2
Spearman’s rank correlation coefficient is rs = 1 –
n(n 2 − 1)

Expectation algebra

For independent random variables X and Y
E(XY ) = E(X )E(Y ), Var(aX ± bY ) = a2 Var(X ) + b2 Var(Y )

24 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller hanalamba1. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $7.77. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

69252 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 15 years now

Start selling