Complete Summary of A Level OCR MEI B Statistics Minor
8 views 0 purchase
Course
Statistics Minor
Institution
OCR
Full Summary from the OCR MEI B B A level Statistics Minor specification. Written by a Cambridge offer-holder and A*A*A* predicted student. Hand-drawn diagrams and detailing included.
Maths Statistics
Give answers to 4sf
Probability
A and B are independent: if I know A will/won’t happen then this won’t affect my estimate
of P(B) and vice versa
P ( A ∪B ) =P ( A )+ P ( B )−P ( A ∩ B )
Mutually exclusive events cannot occur simultaneously
Complementary events sum to 1
A and B are mutually exclusive then P ( A ∩B )=0
A and B are complementary events then P ( A ) + P ( B ) = 1
Notation:
o ∈means is an element of
o ∉ means not an element of
o ∪means union
o ∩ means intersection
o X ∨X ' means the complement of the set X
o n( X ) means the number of elements in set X
o A ⊂B means A is a proper subset of B (cannot be same set)
o A ⊆B means A is a subset of B
o ∅ means a null set
o A' ∪B' ∪C' =( A ∩B ∩C )'
Venn diagrams or contingency tables (two-way tables) can be used to display events
Contingency table:
P ( A ∩ B)
P ( A|B )=
P (B )
If 2 events are independent then
o P ( R ∩ S )=P ( R ) P ( S )
o This can be derived from conditional probability:
P ( A ∩ B)
P ( A|B )=
P (B )
If independent then P ( A|B ) =P ( A )
Substituting this in:
P(A∩B)
P ( A )=
P ( B)
P ( A ∩B )=P ( A ) P(B)
Draw tree diagrams!
There are n! ways to arrange n items
n!
If there are r spaces and n items altogether, there are ways to arrange them, IF
( n−r ) !
order matters (permutation- nPr)
n!
If there are x spaces and n items altogether, there are ways to arrange them,
( n−r ) ! r !
n
removing repeats IF order does not matter (combination nCr or ( ) ¿
r
If there are repeated items, then you divide the total by the factorial of the number of
repeats:
o Eg. Finding anagrams of the word LOLLIPOP
o There are 8 letters
o There are 2 repeated Os, 3 repeated Ls, 2 repeated Ps
, 8!
o Therefore, there are anagrams
2!× 3! × 2!
20
C3 ×2 is not the same as 40C6
, Binomial Distribution
k n−k
P ( E )=nCk × p × q where
o n is the total number of trials
o k is the number of trials satisfying the event
o p is the probability of the event occurring
o q is the probability of the event not occurring
n!
o Remember, nCk=
r ! ( n−r ) !
To apply binomial distribution the following conditions must be met:
o There are a fixed number of trials (n)
o Every trial has only two possible results, success or failure
o The probability of success for each trial is constant (p)
o The trials are independent
You can define a random variable for binomial probability
o Eg. X is the number of 5s rolled after 5 rolls of a die
1
X Bin(5 , )
6
To then indicate the probability of a specific number of the event occurrence, you write:
2 3
1 5
Eg. P ( X=2 )=5 C 2× ×
6 6
Binomial distribution is discrete so it must be drawn as a bar chart, not a smooth curve
E ( X ) =np
Var(X) = npq=np (1− p)
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 saanyav. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $79.12. You're not tied to anything after your purchase.
