S2 Revision Notes Edexcel

A summary of everything you need to know for the S2 exam

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Karina Gahir
S2 EDEXCEL REVISION NOTES
Binomial Distribution
Binomial probability distribution is defined as:
o P(X=r) = nCr x pn x (1-p)n-r
o Distribution is written as: X~B(n,p)
Conditions include:
o Fixed number of trials
o All trials are independent of one another
o Probability of success remains constant
o Each trial much have the same two possible outcomes
E(X) = np
Var(X) = npq [where q = 1 - p]
SD(X) = V ar (X ) = npq
To calculate the probabilities:
o P(X x) = read off the tables
o P(X x) = 1- P(X x-1)
o P(X < x) = P(X x-1)
o P(X > x) = 1- P(X x)
o P(x X y) = P(X y) ­ P(X x-1)
o P(x < X < y) = P(X y) ­ P(X x)
o P(x X < y) = P(X y-1) ­ P(X x-1)
o P(x < X y) = P(X y) ­ P(X x)
Note: If p > 0.5, need to make X~B(n,p) convert to Y~B(n,p)
Example:
If X~B(18,0.9), 0.9 is > 0.5 therefore not on the tables
We want to find P(X > 8)
This will become P(Y < 10) AND Y~B(10,0.1)
Poisson Distribution
Binomial probability distribution is defined as:
e- x r
o P(X=r) = r!
o Distribution is written as: X~Po( )
Conditions include:
o Events occur at random
o All events are independent of one another
o Average rate of occurrence remains constant
o Zero probability of simultaneous occurrences
E(X) =
Var(X) =
SD(X) = V ar (X ) =
To calculate the probabilities:
o P(X x) = read off the tables
o P(X x) = 1- P(X x-1)
o P(X < x) = P(X x-1)
o P(X > x) = 1- P(X x)
o P(x X y) = P(X y) ­ P(X x-1)
o P(x < X < y) = P(X y) ­ P(X x)
o P(x X < y) = P(X y-1) ­ P(X x-1)
o P(x < X y) = P(X y) ­ P(X x)
To approximate the poisson to the binomial, the following conditions have to apply:
o If X~B(n,p) and 1) n is large [n > 50] and
2) p is small [p < 0.1] then, X~Po(np)

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Karina Gahir
Continuous Random Variables
For a probability density function (p.d.f)
b
o P(a < X < b) = f (x) dx
a
o P(X < k) = P(X k)
For a cumulative distribution function (c.d.f)
upper limit
o F(xo) = P(X x o) using a p.d.…read more

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Karina Gahir
Subjective choice by person taking the sample
Non-response
Sampling from an incomplete sampling frame
Sampling Distribution of a statistic
o Parameters are quantities that describe characteristics of a population (e.g. the mean, variance or
proportion that satisfies certain criteria)
o They can be estimated from sample data using quantities called statistics:
For example, if a random sample of size n, X1, ...…read more

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Karina Gahir
Carrying out the tests
o When carrying out a hypothesis test, the stages involved are as follows:
Establish the null (Ho) and alternative (H1) hypotheses
Decide on a significance level (usually given to you in the question)
Collect your suitable data (conditions for this involve random sampling and the items are
independent)
Conduct the test ­ binomial or poisson?
Interpret your results by comparing it to the significant level
If your calculated p > significance level then you do not reject your Ho…read more

Comments

Fabio Ciaschi

I absolutely love you.

Marcus Burch

very good, although you've put on the document var(x) = (b + a)^2/12 rather than (b-a)^2/12 - your proof has the correct result in.

Ragnaros the Firelord

Would give it 10 stars if i could ^

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