Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Title: exam formula for statistics methods
Description: this is the required formula to remember for this subject
Description: this is the required formula to remember for this subject
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
MATH20802: Statistical Methods
Semester 2
Formulas to remember for the final exam
The moment generating function of a random variable X is MX (t) = E [exp(tX)]
...
The moment generating function of a Γ(a, λ) random variable (where a is the shape
a
λ
parameter and λ is the scale parameter) is MX (t) = λ−t
...
θ is an unbiased estimator of θ if E θ = θ
...
n→∞
The bias of θ is E θ − θ
...
θ−θ
2
= 0
...
, N } has the probability
1
mass function p(x) = N for x = 1, 2,
...
∞
The gamma function is defined by Γ(a) =
ta−1 exp(−t)dt
...
The fact that Γ(x + 1) = xΓ(x)
...
1
The beta function is defined by B (a, b) =
ta−1 (1 − t)b−1 dt
...
Γ(a + b)
The probability density function of X ∼ Exp (λ) is fX (x) = λ exp (−λx)
...
The cumulative distribution function of X ∼ N (0, 1) is Φ(x)
...
The Type II error of H0 : µ = µ0 versus H0 : µ = µ0 occurs if H0 is accepted when in
fact µ = µ0
...
The power function of H0 : µ = µ0 versus H0 : µ = µ0 is Π(µ) = Pr (RejectH0 | µ)
...
, Xm be a random sample from a normal population with mean µX and
2
variance σX assumed known
...
, Yn be a random sample from a normal
2
population with mean µY and variance σY assumed known
...
The rejection region for H0 : µX = µY versus H1 : µX = µY is
|X −Y |
2
σX
m
+
≥ zα/2
...
2
σY
n
The rejection region for H0 : µX ≥ µY versus H1 : µX < µY is
X −Y
2
σX
m
+
2
σY
n
≤ −zα
...
, Xn from a distribution with the probability
density function f (x; θ), the Neyman-Pearson test rejects H0 : θ = θ1 versus H1 : θ = θ2
if
n
L (θ1 )
=
L (θ2 )
f (Xi ; θ1 )
i=1
n
i=1
for some k
Title: exam formula for statistics methods
Description: this is the required formula to remember for this subject
Description: this is the required formula to remember for this subject