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Q1: 1. Probability distribution of a sum of two continuous random variables. Exampleswith Gaussian normal, exponential, uniform distributions of summands.See Answer
Q2: 2. Joint probability distribution of several random variables: discrete case. Exam-ples of multivariate distributions.See Answer
Q3: 3. Joint probability distribution of several random variables: continuous case. Ex-amples of multivariate distributions.See Answer
Q4: 4. Probability distribution of a function of a random variable (Y = ƒ(X)). Exam-ples.See Answer
Q5: 5. Probability distribution of a sum of two integer random variables. Examples foridentically distributed summands with Poisson, geometric, uniform distributions.See Answer
Q6: 6. Probability distribution of a sum of two continuous random variables. Exampleswith Gaussian normal, exponential, uniform distributions of summands.See Answer
Q7: 7. Mathematical expectation (both discrete and continuous cases). Its properties(with proofs). Examples.See Answer
Q8: 9. Covariance and correlation (both discrete and continuous cases), their properties.Examples. 8. Variance (both discrete and continuous cases) and its properties (with proofs).Examples.See Answer
Q9: 9. Covariance and correlation (both discrete and continuous cases), their properties.Examples.See Answer
Q10: 10. Binomial distribution: its origins, mathematical expectation, variance.See Answer
Q11: 11. Discrete uniform distribution: its origins, mathematical expectation, variance (withproofs).See Answer
Q12: 12. Poisson distribution: its origins, mathematical expectation, variance (with proofs).See Answer
Q13: 13. Hyper-geometric distribution: its origins, mathematical expectation, variance (withproofs).See Answer
Q14: 14. Geometric distribution: its origins, mathematical expectation, variance (with proofs).See Answer
Q15: 15. Continuous uniform distribution, its mathematical expectation, variance (withproofs).See Answer
Q16: 24. Simple linear regression (Gauss-Markov model): estimation, prediction.See Answer
Q17: 26. Chi-square test of independence for a contigency table. Examples.See Answer
Q18: 16. Exponential distribution, its mathematical expectation, variance (with proofs).See Answer
Q19: 17. Normal (Gaussian) distribution, its mathematical expectation, variance (with proofs).See Answer
Q20: 18. De Moivre – Laplace theorem. Central limit theorem. Examples (with proofs).See Answer

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