Week 1 Flashcards
A RV X is said to be Absolutely Continuous if
There exists a non negative function f, such that for any open set B
(such an f is the PDF)
For a PDF f, the support of f is
The set of points where f is positive
Range of RV
RV X with CDF F has characteristic function
For continuous dist, P(X=x) = ?
0 for al x in range of X
Kernel of PDF
Pdf with normalization constants factored out(?)
Kernel of Gaussian dist
Location parameter
μ is a location parameter if F(x;μ) = F(x-μ;0) or equivalently for PDF
Scale parameter
σ is a scale parameter if
F(x;σ) = F(x/σ;1) or for a PDF f(x;σ) = (1/σ)f(x/σ;1)
Shape parameter
If a parameter is not location or scale
what is a statistic
Any measurable function of the sample such that
Empirical quantile formula
After ordering data in ascending order
Descriptive analysis
Analysis only using summary statistics
A RV X is said to be discrete if
The range of X can be counted
Finding scale or location params in dist
Location: look for additive terms
Scale: look for multiplicative terms
A distribution is said to be identifiable if
No 2 values of a parameter generate the same dist
Scale/rate parameter for expo dist
Precision for normal dist
generally1 over var of dist: 1/σ2
Σ
Cov matrix
2 entries of a multivariate random vector (Xi, Xj) are independent if
Σi,j = 0 for normal dist
Converse holds for all dist
Almost sure convergence
Convergence in P
Almost surely convergence ε
Convergence in probability ε
n’th absolute moment of continuous RV
