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Orthogonal Transformation of Independent Normal Random Variables
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Classroom Contents
Transformations of Random Variables
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- 1 Transformations: Discrete Univariate Random Variables
- 2 Transformations: CDF Technique
- 3 Transformations: Univariate Change of Variable
- 4 Transformations: Multivariate to Univariate CDF Technique
- 5 Transformations: Discrete Multivariate Sum of Binomial Random Variables
- 6 Transformations: Multivariate Change of Variable
- 7 Transformations: Product of Uniform Random Variables
- 8 Transformations: Ratio of Standard Normal Random Variables to a Cauchy Random Variable
- 9 Transformations: Uniform Random Variable to a Cauchy Random Variable
- 10 Transformations: t Random Variable to a Beta Random Variable
- 11 Transformations: Sums and Ratios of Gamma Random Variables
- 12 Transformations: Derive the Joint pdf of Order Statistics
- 13 Transformations: F Random Variable to a Beta Random Variable
- 14 Transformations: Sums and Ratios of Exponential Random Variables
- 15 Transformations: Sums of Chi square Random Variables
- 16 Transformations: Xj has a Continuous and Strictly Increasing CDF
- 17 Transformations: X~Unif[0,2] to Y=(X/(1-X))**2
- 18 Transformations: Sums of Binomial Random Variables with Unequal Proportions
- 19 Linear Transformations of Random Vectors
- 20 Orthogonal Transformation of Independent Normal Random Variables
- 21 Sample Mean and Variance are Independent if Data are Normal
- 22 Ratio of Independent Gamma rv's to a Beta Prime Distribution
- 23 Beta Prime Random Variable to a Beta Distribution and Vice Versa
- 24 Multivariate Normal Random Variable transformed to a Multivariate Uniform Random Variable
- 25 Distribution for the Sum of Negative Binomial Random Variables Using the MGF
- 26 Derivation of the Dirichlet Distribution
- 27 Distribution of the Mid Range Statistic
- 28 Example using Vandermonde's Identity: Sum of 2 Binomial Random Variables w/ Equal p.
- 29 Crazy Transformation: y=sin(x)^2 where x~unif(0,2Pi)
- 30 Transform 2 Normal RVs to a Rayleigh RV (part 1/2)
- 31 Transform 2 Normal RVs to a Rayleigh RV (part 2/2)
- 32 Comparing Adverse Event Rates Between Treatment Arms
- 33 Joint Distribution of the Mid-Range and the Range
- 34 Prove Pearson's Goodness of Fit Test Statistic limits to a Chi-sq Distribution
- 35 Show that R & Theta are Independent in Polar Coordinates
