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 :

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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