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# Probability  Statistics Symbols

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 :
 Symbol Symbol Name Meaning/Definition> Example 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) σ2 Variance Variance of population values σ2 = 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 σx = 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) ρX,Y Correlation Correlation of random variables X and Y ρX,Y = 4 18) ∑ Summation Summation - sum of all values in range of series ∑ Xi (i = 1 to 4) = x1+x2+x3+x4 19) Mo Mode Value that occurs most frequently in population 20) MR Mid-range MR = (xmax+xmin)/2 21) Md Sample median Half the population is below this value 22) Q1 Lower / first quartile 25% of population are below this value 23) Q2 Median / second quartile 50% of population are below this value = median of samples 24) Q3 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) s2 Sample variance Population samples variance estimator s2 = 9 27) s Sample standard deviation Population samples standard deviation estimator s = 4 28) zx Standard score zx = (x-x) / sx 29) X ~ Distribution of X Distribution of random variable X X ~ N(0,4) 30) N(μ,σ2) 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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