Week 1 Flashcards

1
Q

A RV X is said to be Absolutely Continuous if

A

There exists a non negative function f, such that for any open set B

(such an f is the PDF)

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2
Q

For a PDF f, the support of f is

A

The set of points where f is positive

Range of RV

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3
Q

RV X with CDF F has characteristic function

A
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4
Q

For continuous dist, P(X=x) = ?

A

0 for al x in range of X

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5
Q

Kernel of PDF

A

Pdf with normalization constants factored out(?)

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6
Q

Kernel of Gaussian dist

A
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7
Q

Location parameter

A

μ is a location parameter if F(x;μ) = F(x-μ;0) or equivalently for PDF

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8
Q

Scale parameter

A

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)

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9
Q

Shape parameter

A

If a parameter is not location or scale

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10
Q

what is a statistic

A

Any measurable function of the sample such that

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11
Q

Empirical quantile formula

A

After ordering data in ascending order

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12
Q

Descriptive analysis

A

Analysis only using summary statistics

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13
Q

A RV X is said to be discrete if

A

The range of X can be counted

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14
Q

Finding scale or location params in dist

A

Location: look for additive terms

Scale: look for multiplicative terms

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15
Q

A distribution is said to be identifiable if

A

No 2 values of a parameter generate the same dist

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16
Q

Scale/rate parameter for expo dist

A
17
Q

Precision for normal dist

A

generally1 over var of dist: 1/σ2

18
Q

Σ

A

Cov matrix

19
Q

2 entries of a multivariate random vector (Xi, Xj) are independent if

A

Σi,j = 0 for normal dist

Converse holds for all dist

20
Q

Almost sure convergence

A
21
Q

Convergence in P

A
22
Q

Almost surely convergence ε

A
23
Q

Convergence in probability ε

A
24
Q

n’th absolute moment of continuous RV

A
25
Q

Convergence in r mean

A
26
Q

Convergence in distribution

A
27
Q

Relate 3 kinds of P convergence

A
28
Q

Slutsky’s theorem

A
29
Q

Continuous mapping theorem

A
30
Q

Weak LLN

A
31
Q

Strong LLN

A
32
Q

CLT univariate

A
33
Q

Markov’s inequality

A
34
Q

Chebyshev’s inequality

A
35
Q

Jensen’s inequality

A
36
Q

Holder’s inequality

A
37
Q

THERE IS A LIST ON KEATS

A

Of things that aren’t examinable