Class Test 1 Flashcards
General formula, E(Y), V(Y) for binomial?
P(Y=y) = (n y)p^y.q^(n-y) E(Y) = np V(Y) = npq
General formula, E(Y), V(Y) for geometric?
p(y) = q^(y-1).p E(Y) = 1/p V(Y) = (1-p)/p^2
What is y in geometric distribution?
The number trial first success occurs
P(Y>y) for geometric distribution?
q^y
General formula, E(Y), V(Y) for negative binomial?
p(y) = (y-1 r-1).p^r.q^y-r E(Y) = r/p V(Y) = r(1-p)/p^2
General formula, E(Y), V(Y) for poisson?
P(Y=y) = (e^-λ.λ^y)/y! E(Y) = λ V(Y) = λ
General formula, E(Y), V(Y) for uniform?
f(y) = 1/(θ2-θ1) for y between theta
0 elsewhere
E(Y) = (θ1+θ2)/2
V(Y) = ((θ2-θ1)^2)/12
General formula, E(Y), V(Y) for normal?
Z=(Y-μ)/σ
E(Y) = μ
V(Y) = σ^2
General formula, E(Y), V(Y) for gamma?
See notes for GF
E(Y) = αβ V(Y) = αβ^2
General formula, E(Y), V(Y) for chi-square?
Gamma formula with α=v/2 and β=2
E(Y)=v
V(Y)=2v
What is chi square distribution used for?
Determining likelihood that an observer distribution is due to chance
General formula, E(Y), V(Y) for exponential distribution?
Gamma formula with α=1
Tf f(y) = (1/β)e^(-y/β) (see notes)
E(Y) = β V(Y) = β^2
What is definition 4.13 regarding moments? (Both parts and equations)
If Y is a CRV, then the kth moment about the origin is given by:
μ’k = E(Y^k) k=1,2…
The kth moment about the mean, or the kth central moment, is given by:
μk = E[(Y-μ)^k] k=1,2…
(For k=1, μ’1=μ, and for k=2, μ2=V(Y))
How many ways are there to place ‘n’ distinct objects in a row?
Permutation since order matters, tf n!
Number of ways to select 4 balls without replacement from a container with 15 distinct balls?
15choose4=1365
Given 10 maths teachers, need to choose 3 for a committee, what is the probability that Mr A, B and C are chosen?
(number of ways ABC can be selected)/total number of combos of maths teachers
=1/(10choose3)=1/120
See and learn
Table on other side of permutations notes
Define population?
The large body of data that is the target of our interest?
What is a sample?
A subset of the population
Define the following:
1) experiment
2) event
3) simple event
4) compound event
5) sample space
1) the process by which an observation is made
2) the outcome of an experiment
3) an event that cannot be decomposed
4) an event that can be decomposed into simple events
5) set of all possible sample points
What is a discrete sample space?
A SS with a finite/countably finite number of distinct sample points
What is the mn rule?
With m elements (a1…am) and n elements (b1…bn) it is possible to form m.n number of pairs containing one element from each group
Define permutation?
The number of ways of ordering n distinct objects taken r at a time (Pnr)
What does Cnr stand for?
The number of combinations of n objects taken r at a time is the number of subsets, each of size r, that can be formed from the n objects
