4. Transformations

Question 1

Theorem 4.1
Univariate transformation.

Question 2

Definition 4.1
Standard Normal

Question 3

Definition 4.2
General Normal.

Question 4

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

Question 5

Definition 4.3
Lognormal.

Question 6

Definition 4.4
Chi-squared.

Question 7

Definition 4.5
Joint distribution.

Question 8

Definition 4.6
Multivariate distribution function.

Question 9

Marginal distribution.

Question 10

Definition 4.7
Covariance.

Question 11

Lemma 4.2
Independence implies zero covariance.
Defn of Correlation

Question 12

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

Question 13

Corollary 4.1
correlation inequality.

Question 14

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

Question 15

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

Question 16

Theorem 4.2
Multivariate transformation.

Question 17

Definition 4.8
The Beta distribution.

Question 18

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

Question 19

Definition 4.9
Multivariate normal distribution.

Question 20

Theorem 4.3
Density of Multivariate Normal distribution.

Question 21

Multivariate normal distribution properties.

Question 22

Theorem 4.4
Fisher’s Theorem

Question 23

Definition 4.10
F-distribution.

Question 24

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