Statistics [Lectures]

 

Lecture #1

Basic term of the probability, P(A) = m / n, when n is total count of events and m is count of target event.


How to get combinations count, 


C, order and copied isn't important.

A, order isn't important.

P, all is important.


Probability of dependent events is P(A * B) = P(A) * P(B|A)

Probability of independent events is P(AB) = P(A) * P(B)


Logic OR is P(C) = P(A) + P(B)

Logic AND is P(C) = P(A) * P(B)


If event A can be if array of events B us true is

P(A) = P(B1) * P(A|B1) + ... + P(Bn) * P(A|Bn)


Bayes theorem is

P(B|A) = P(A|B) * P(B) / P(A)


Lecture #2

 

  1. Binomial distribution
    1. M(n) = n * p
    2. D(n) = n * p * q, where q = 1 - p 
    3. sd = sqrt(D)
  2. ... 
    1. Mean = М (Х) = (x1* p1) + (x2 * p2) + … + (xn * pn)
    2. Standard deviation =      

  1. Discrete distribution. Probability of event will be k times into n tests.
    1. Binomial distribution (Bernoulli equation)
      1. P(k) = Ckn * pk * qn-k
      2. np - q <= k0 <= np + q, to get event that have high possible chance ... 
    2. Poisson's equation
      1. P(k)=λk * e−λ/ k!, where λ = np
    3. Laplace expansion
    4. ...
    5. ...

Lecture #3





Lecture #4


Two distribution of probability is discrete and continuous. DPD is only counting values. CPD is values from the range from the Real numeric.

Each distribution have cumulative function f(x) that can take probability to each value and have first derivative of this function f'(x) - ... .

How to get it, example:
  1. Collect data each day and draw them on the chart;
  2. Get many data that provide cumulative function;
  3. Get integral of it to get square of figure;
  4. It will be function of probability distribution;
Example of the function of the normal probability is 


where in the range of three σ we have 99.72% of all values probability, but it only for perfect normal distribution. Mode and mean is equal here.

Standard normal distribution where σ = 1, σ2 = 1, ... All normal distribution possible to convert to SND and use table to get probability values that we are need.

If X ~ N(µ,σ) when Z = (X - µ) / σ ~ N(0,1)


Central limit theorem - 


Uniform distribution - 


Lecture #8


  • Correlation analyze is method to check two (or more) variables for linear dependence;
  • r = 0 isn't that we haven't linear dependence there only;
  • If we have correlation between two variable, possible that it isn't truth, because third hidden variable is here (hospital count and cafe count, third - peoples count into the city);
  • Possible what we have random dependence without really correlation while correlation coefficient is high;
  • Possible to confuse cause and effect;
  • We don't know how its fast (y' of linear function);
  • We don't understand how it works at time line;
  • Covariance for fast check ... ;
  • Examples: Spearman's rank correlation coefficient (don't need normal distribution), Pearson correlation coefficient;

Lecture #9


  • ...


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