Exercise Book to "Probability Theory with Simulations"
András Vetier
Poly-hyper-geometrical distribution
Polynomial distribution
Hyper-geometrical distribution
Geometrical problems, uniform distributions
Generating a random variable with a given continuous distribution
Expected value of discrete distributions
Exponential distribution
Uniform distribution (discrete)
Infinite sequences of events
U-tests
Generating a random variable with a given discrete distribution
Uniform distributions
Chi-square-test for fitness
Properties of the expected value, variance and standard deviation
Median
Distribution function
Linear regression
Poisson-processes
The RAND function
Higher dimensional discrete random variables and distributions
Normal distributions
Normal distributions in two-dimensions
Moments of a discrete random variable
Outcomes and events
Beta distributions in two-dimensions
Cauchy distribution
Beta distributions
Distributions derived from normal
Independence of events
Distributions of some functions of random numbers
Conditional relative frequency and conditional probability
Density function
The table structure of Excel
Transformation of discrete distributions
Expected value of a function of a continuous random variable
Transformation from line to line
Discrete random variables and distributions
The RANDBETWEEN function
Standard deviation,
T-tests
Independence of random variables
Random numbers
Limit theorems to normal distributions
Classical problems
Arc-sine distribution
Generating a two-dimensional random variable
Relative frequency and probability
Projections and conditional distributions for discrete distributions
Basic properties of probability
Simulating an event with the IF function
Expected value of continuous distributions
F-test for equality of variances (of standard deviations)
Binomial distribution
Drawing with or without replacement. Permutations
Poisson-distribution
Continuous random variables
Confidence intervals
Empirical distribution function
Test with ANOVA
Two-dimensional random variables and distributions
Negative binomial distribution
Gamma distribution
Combinatorial exercises
Sums of random variables. Convolution
Regression
Mode of a distribution
This exercise-book follows the structure of my text-book entitled http://www.math.bme.hu/~vetier/df/index.html Probability Theory with Simulations, containing the usual material taught at probability theory and statistics courses at most universities of the world. The same way, as in the text-book, there are five parts:
Probability of events
Discrete distributions
Continuous distributions in one-dimension
Two-dimensional continuous distributions
Statistics
Budapesti Műszaki és Gazdaságtudományi Egyetem Természettudományi Kar
Budapesti Műszaki és Gazdaságtudományi Egyetem Természettudományi Kar
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2013-11-30
Creative Commons Attribution Non-Commercial No Derivatives (CC-BY-NC-ND-3.0) Magyarország
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András Vetier
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