THE TOPICS ORDER OF MATHEMATICAL STATISTICS I
1. Counting rules.
Sigma
Notation.
Factorial
Notation
Newton
Binomium
Multiplication
In Counting Rules
Permutation
Cycle
permutation
Permutation
with same elements
Combination
2. Experiment,
Sample space, and Event
Definition
of probability:
Probability
Complement.
Probability
of union of two events or more
Conditional
Probability
Probability
of mutual exclusive events
Probability
of stochastic events
3. Bayes
Theorem
Random
variables
Probability
cumulative function
Probability
density function
4. Expected
values
Usage of
Expected values
Moment
generating function
Chebysev
Equation
5. Discrete
random variables distributions I
Bernoulli
distribution
Binomial
distribution
Hypergeometric
distribution
6. Discrete
random variables distributions II
Geometric
distribution.
Negative
Binomial distribution
Poisson
distribution
7. Continuous
random variables distributions I.
Normal (Gaussian)
distribution
Gamma
distribution
Chi-Square
distribution
8.Continuous
random variables distributions II.
Exponential
distribution
Weibull
distribution
Pareto
distribution
Uniform
distribution
9.Joint
and marginal distribution
Conditional
Distribution
Coefficient
correlation
10.
Random variables stochastics
Random
variables transformation
Ordered
statistics
11.Sampling
distribution
Definition
and basic concept
Means
sampling distribution
Proportion
sampling distribution
Difference
and Sum sampling distribution
12.Problem
solved.
URUTAN MATERI STATISTIKA
MATEMATIS I
1.Kaidah Pencacahan.
Notasi sigma.
Notasi Faktorial.
Binom Newton.
Aturan Perkalian.
Permutasi.
Permutasi Siklis.
Permutasi dengan Beberapa Unsur Sama.
Kombinasi.
2.Percobaan, Ruang Sampel, dan Kejadian.
Definisi Peluang: - Frekuensi Nisbi,
- Pendekatan Klasik.
- Kolomogrof.
Kisaran Peluang.
Komplement Peluang.
Peluang gabungan dua kejadian.
Peluang dua kejadian bersyarat (peluang bersyarat).
Peluang dua kejadian saling bebas.
Peluang dua kejadian saling lepas.
3.Dalil bayes.
Variabel random.
Fungsi kepadatan peluang.
4.Ekspektasi matematis.
Kegunaan ekspektasi matematis.
Fungsi pembangkit momen.
Ketidaksamaan Chebysev.
5.Distribusi peubah acak diskrit I
Distribusi bernoulli.
Distribusi binomial.
Distribusi hipergeometrik.
6.Distribusi peubah acak diskrit I
Distribusi geometrik.
Distribusi binomial negatif.
Distribusi poisson.
7.Distribusi peubah acak kontinu I.
Distribusi normal (Gaussian).
Distribusi gamma.
Distribusi chi-kuadrat.
8.Distribusi peubah acak kontinu II.
Distribusi Eksponensial.
Distribusi Weibull.
Distribusi Pareto.
Distribusi Seragam.
9.Distribusi Bersama.
Distribusi Bersyarat.
Koefisien Korelasi.
10.Kebebasan variabel-variabel random.
Transformasi peubah acak.
Statistika urutan.
11.Distribusi sampling
Pengertian dan konsep dasar.
Distribusi mean-mean sampling.
Distribusi proporsi sampling.
Distribusi perbedaan dan penjumlahan dari sampling.
12.Soal-soal.
