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Short summary statistics for pre-master Tilburg University (350931-B-6)
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Short summary to study and practice for the course Statistics for pre-master.
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Week 1 (Globale introductie)• Introduction probability theory and Discrete random variables
- Density function, Cumulative distribution function
- Expectation, variance, standard deviation
• Families of discrete distributions (Bernoulli distribution, Binomial distribution)
Week 2 (Continues random variables)
• Continues random variables (CH 8)
- Density function, cumulative distribution function, Expectation and variance
• Variance of continues random variables (CH 10 en 10.3)
• Families of continues random variables
- Uniform distribution and Normal distribution
Week 3 (Sampling theory)
• Joint probability distributions (Ch 11)
- Density function. Covariance, correlation coefficient.
• Sampling theory (Ch 12 and Ch 13)
- Random samples with replacement.
- Sample statistics & estimators (expectation, variance, distribution, central limit theorem).
Week 4 (Statistical procedures when σ is known)
• Inferential statistics (Ch 15 – 25, today Ch 15)
- Initial approach to statistical procedures.
- Point and interval estimation of μ when σ is known.
- Hypothesis testing with respect to μ when σ is known:
- five step procedure (three testing problems) & p-value.
Week 5 (Statistical procedures when σ is unknown)
• Statistical procedures for μ when σ is unknown (Ch 16).
- Standardized sample mean and t-distribution. Confidence intervals and tests
• Statistical procedures for proportion p (Ch 16).
- Estimator sample proportion (mean, variance, distribution). Confidence intervals and tests
• Statistical procedures for variance σ2 (Ch 17).
- Estimator sample variance and χ2 distribution. Confidence intervals and tests
Week 6 (Scatterplot. Samples and simple linear regression model)
• Scatter plot, sample covariance and sample correlation coefficient (more information see ch 5).
• Simple linear regression model (Ch 19)
- Estimation of the coefficients,
- Model assumptions,
- Interpretation of the coefficients,
- Confidence intervals and tests for the slope.
Week 7
• Simple linear regression (Ch 19)
- Analysis of variance (Anova)-table and coefficient of determination
- Special application: market model
- Conclusions about Y and E(Y)
- Residual analysis
,WEEK 1
• Introductie probability theory
• Discrete random variables
o Density function, Cumulative distribution function
o Expectation, variance, standard deviation
• Families of discrete distributions (Bernoulli distribution, Binomial distribution)
Bernoulli experiment: random experiment with only two outcomes called S (success) and F (failure).
Binomial experiment: Bernoulli experiment with unlimited possible repetitions
WEEK 2
• Continues random variables (CH 8)
o Density function, cumulatieve distribution function
o Expectation and variance
• Variance of continues random variables (CH 10 en 10.3)
• Families of continues random variables
o Uniform distribution
o Normal distribution
, Expectation and variance (continuous random variable)
Normal distribution to Standard Normal distribution
Special quantiles of N(0,1)
Verschil Discrete variabelen en continous variabelen
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