Probability Statistics Symbols
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This section is about the symbols of probability statistics.Probability statistics Symbols : Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we are not certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1, we call probability.The higher the probability of an event, the more certain we are that the event will occur. Thus, probability statistics in an applied sense is a measure of the likeliness that a (random) event will occur. Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.
Probability statistics Symbols :




1)P (A)  Probability function.  Probability of event A.  P(A) = 0.5 
2) P(A∩ B)  Probability of events intersection  Probability that of events A and B  P(A∩B) = 0.6 
3) P(A ∪ B)  Probability of events union  Probability that of events A or B  P(A∪B) = 0.9 
4) P(A  B)  Conditional probability function  Probability of event A given event B occurred  P(A  B) = 0.2 
5) f (x)  Probability density function (pdf)  P(a ≤ x ≤ b) = ∫ f (x) dx  
6) F(x)  Cumulative distribution function (cdf)  F(x) = P(X ≤ x)  
7) μ  Population mean  Mean of population values  μ = 20 
8) E(X)  Expectation value  Expected value of random variable X  E(X) = 20 
9) E(X  Y)  Conditional expectation  Expected value of random variable X given Y  E(X  Y=2) = 5 
10) var(X)  Variance  Variance of random variable X  var(X) = 4 
11) σ^{2}  Variance  Variance of population values  σ^{2} = 9 
12) std(X)  Standard deviation  Standard deviation of random variable X  std(X) = 2 
13) σ_{ x}  Standard deviation  Standard deviation value of random variable X  σ_{x} = 2 
14)x^{˜}  Median  Middle value of random variable x  x^{˜}=6 
15) cov(X,Y)  Covariance  Covariance of random variables X and Y  cov(X,Y) = 6 
16) corr(X,Y)  Correlation  Correlation of random variables X and Y  corr(X,Y) = 3 
17) ρ_{X,Y}  Correlation  Correlation of random variables X and Y  ρ_{X,Y} = 4 
18) ∑  Summation  Summation  sum of all values in range of series  ∑ X_{i} (i = 1 to 4) = x_{1}+x_{2}+x_{3}+x_{4} 
19) Mo  Mode  Value that occurs most frequently in population  
20) MR  Midrange  MR = (x_{max}+x_{min})/2  
21) Md  Sample median  Half the population is below this value  
22) Q_{1}  Lower / first quartile  25% of population are below this value  
23) Q_{2}  Median / second quartile  50% of population are below this value = median of samples  
24) Q_{3}  Upper / third quartile  75% of population are below this value  
25) X^{}  Sample mean  Average / arithmetic mean  x^{} = (2+5+9) / 3 = 5.333 
26) s^{2}  Sample variance  Population samples variance estimator  s^{2} = 9 
27) s  Sample standard deviation  Population samples standard deviation estimator  s = 4 
28) z_{x}  Standard score  z_{x} = (xx) / s_{x}  
29) X ~  Distribution of X  Distribution of random variable X  X ~ N(0,4) 
30) N(μ,σ^{2})  Normal distribution  Gaussian distribution  X ~ N(0,6) 
31) U(a,b)  uniform distribution  equal probability in range a,b  X ~ U(0,8) 
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