4. Transformations Flashcards

1
Q

Theorem 4.1
Univariate transformation.

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2
Q

Definition 4.1
Standard Normal

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3
Q

Definition 4.2
General Normal.

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4
Q

Lemma 4.1
If X, Y are two independent standard Normal, then X + Y ~…

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5
Q

Definition 4.3
Lognormal.

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6
Q

Definition 4.4
Chi-squared.

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7
Q

Definition 4.5
Joint distribution.

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8
Q

Definition 4.6
Multivariate distribution function.

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9
Q

Marginal distribution.

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10
Q

Definition 4.7
Covariance.

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11
Q

Lemma 4.2
Independence implies zero covariance.
Defn of Correlation

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12
Q

Lemma 4.3
If X and Y defined on same probability space with finite second moments, then Var(…) = …

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13
Q

Corollary 4.1
correlation inequality.

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14
Q

Corollary 4.2
If X_1, …, X_n independent with finite second moments, then Var(…) = …

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15
Q

Lemma 4.4
Means, variances, and covariances of Multinomial distribution.

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16
Q

Theorem 4.2
Multivariate transformation.

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17
Q

Definition 4.8
The Beta distribution.

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18
Q

Lemma 4.5
If two gamma dist. are independent, then…

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19
Q

Definition 4.9
Multivariate normal distribution.

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20
Q

Theorem 4.3
Density of Multivariate Normal distribution.

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21
Q

Multivariate normal distribution properties.

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22
Q

Theorem 4.4
Fisher’s Theorem

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23
Q

Definition 4.10
F-distribution.

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24
Q

Lemma 4.6
PDF of Y~F_{m, n}

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