Stats S1
Chap 1
Worksheet 1 🏁
Ex 1 : Probability tree adding across
Ex 2: : we have a situation of prob, want to find a value using x
Cours
1) Definitions and concepts
Outcome, sample space, event, elementary event, partition
2) Set theories/ operations on sets
Complement
Union
Intersection
Distribution Law
De Morgan's Law
3) Probability measures
Must satisfy 3 axioms
Probability properties (between 0 and 1, empty event,
4) Law of total probabilities
with Ai and B
Special case
5) Probability for countable sample space
simple formula to calculate P(A°
Uniform sample space ⚠
6) Conditional probability
formula
Bayes formula
7) Proving independence
using intersection
using conditional prob
8) Counting method
Ex 3: Using prop if independance to find unknown value
Ex 4 : counting method use permutation
Chap 2
Worksheet 2 🏁
Ex 1: 1) ❓ 2) ✅ 3) ✅
Ex 2 ✅
Ex 3 ⚠
Ex 4) q1) continuity on d? ❓ q2) ✅
Ex 5: q1) CDF value at the end ❓ 2) ⚠ 3) ⚠
Ex 6 ♻
Ex 7 ♻
Ex 8 ⭐
Ex 9
Ex 10
Ex 11 no need
Ex 12 no need
Chap 3 - 4
Extra practice
Midterm 2020
Cours
Cours "pdf Chap 3 & 4 in english"
Chap 5
Cours
Ex 4 ⭐
Part 2- Approximation
Binomial by a Poisson
Binomial by a Normal
Central limit theorem
Part 2- Joint distributions of discrete r.v
1) ✅ / Q2 ❓ / Q3 : ✅
1) ✅ / 2) ✅
Q1 ✅ / Q2 on ❓ a trouvé ou 22+x?
❓
Ex 1: ✅ determine CDF / play with Bernouilli and Geometric find the distribution
Ex 5 : Find the CDF function using equivalence
Worksheet 3 🏁
Chap 3: Introduction to Sampling
Explain the context of inferential stats
Formalisation in letter p6
Study the quality of the estimator: E(X) and Var(X) (p8)
Methodology: (p10)
Notation (p12)
Chap 4: Pointwise estimation
methodology (p19)
Properties of an estimator (p26) / Bias (unbiased and asymptotically unbiased) / Consistent estimator
Comparing estimators (p28)
Common estimators (p29)
Sample mean / sample variance (biased and unbiased)
sample frequency p32?
Methods
Method 1: Using natural estimator (p34)
If no natural estimator use Method 2: Method of Moments (p39)
Method 3: Maximum likelihood estimator (p43)
Ex 1 : Q1 ✅
Ex 2 MLE log✅
✅compris mais quand meme refaire
Ex 3: log pour fonction continue / max 🔒
Worksheet 4 🏁
Ex 1 - build confidence interval how do I find the values at the end??? ❓
Ex 2 - build CI using case 2 - bilateral and unilateral ✅
Ex 4 - build CI using case 3 ✅
Ex 5 - Using case 4 - poisson law ✅
Ex 6 - playing with n ✅