Studied by 4 people
which distribution can be approximated as another?
binomial as Poisson
when does this approximation work, and what is λ?
when p gets smaller, and n gets bigger and λ= E(x)/ the mean
what characterises a Poisson distribution?
the mean and variance are equal
how to calculate variance
mean of the squares-square of the mean
E(aX+b)=
aE(X)+b
Var(aX+b)=
a² Var(X)
4 conditions that must be met for binomial distribution to work
2 mutually exclusive outcomes
fixed number of trials
each event is independent of the one before
probability of success is constant
4 conditions that must be met for Poisson distribution to work
event occurs randomly in space/time
events cannot occur simultaneously
each event is independent of the one before
the mean remains constant
if X and Y are Poisson distributions, how to calculate X+Y?
X+Y∼Po(sum of means)
how to calculate: P(x≥n) must be <p
P(x≤n-1) must be >(1-p)
two hypotheses needed for hypothesis testing
H₀, the null hypothesis and H₁, the alternative hypothesis
5 steps in a hypothesis testing question
let variable X= ?
state H₀ and H₁
state distribution and find probability
compare probability to significance level
state conclusion in context
formula for Χ²
∑(Oᵢ²/Eᵢ) -N (where N is number of trials)
how to generally calculate degrees of freedom
number of cells (after combining) - number of constraints
what counts as a constraint
estimating a parameter or number of trials
what does ν represent
number of degrees of freedom
what does χ²₃ represent
the family of χ² distributions with 3 degrees of freedom
how to combine the table whilst using a Χ² test
no expected value is allowed to be <5
how to estimate p for a binomial distribution
p= (number of successes)/(number of attempts) or
p= Σ(r x fᵣ)/(N x n)
how to estimate λ for a Poisson distribution
calculate it as if it were the mean of a frequency table
how to do a Χ² test on observed data
calculate p or λ, then use this to generate expected frequencies, then conduct the test as normal
how to calculate expected values for each box in a contingency table
Eᵢ= (row total x column total)/ grand total
how to calculate ν for a contingency table
ν = (no of rows-1)(no of columns-1)
