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Probability Symbols

Probability Symbols - A Complete Guide | ORCHIDS

Probability Symbols:

Probability symbols are integral in probability theory, with (P) denoting probability and (A') representing the complement of event (A). Notable symbols include (μ ) for expected value and (σ2) for variance. Understanding these symbols is crucial for interpreting probabilities and making informed decisions in various fields.

Probability and Statistics symbols table

 

Symbol

Name of Symbol 

Meaning / definition

P(A)

probability function

probability of event A

P(A ∩ B)

probability of events intersection

probability that of events A and B

P(A ∪ B)

probability of events union

probability that of events A or B

P(A | B)

conditional probability function

probability of event A given event B occurs

f (x)

probability density function (pdf)

P(a ≤ x ≤ b) = ∫ f (x) dx

F(x)

cumulative distribution function (cdf)

F(x) = P(X≤ x)

μ

population mean

mean of population values

E(X)

expectation value

expected value of random variable X

E(X | Y)

conditional expectation

expected value of random variable X given Y

var(X)

variance

variance of random variable X

σ2

variance

variance of population values

std(X)

standard deviation

standard deviation of random variable X

σX

standard deviation

standard deviation value of random variable X

median symbol

median

middle value of random variable x

cov(X,Y)

covariance

covariance of random variables X and Y

corr(X,Y)

correlation

correlation of random variables X and Y

ρX,Y

correlation

correlation of random variables X and Y

summation

summation - sum of all values in range of series

∑∑

double summation

double summation

Mo

mode

value that occurs most frequently in population

MR

mid-range

MR = (xmax + xmin) / 2

Md

sample median

half the population is below this value

Q1

lower / first quartile

25% of population are below this value

Q2

median / second quartile

50% of population are below this value = median of samples

Q3

upper / third quartile

75% of population are below this value

x

sample mean

average / arithmetic mean

s 2

sample variance

population samples variance estimator

s

sample standard deviation

population samples standard deviation estimator

zx

standard score

zx = (x-x) / sx

X ~

distribution of X

distribution of random variable X

N(μ,σ2)

normal distribution

gaussian distribution

U(a,b)

uniform distribution

equal probability in range a,b

exp(λ)

exponential distribution

f (x) = λe-λx , x≥0

gamma(c, λ)

gamma distribution

f (x) = λ c xc-1e-λx / Γ(c), x≥0

χ 2(k)

chi-square distribution

f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) )

F (k1, k2)

F distribution

 

Bin(n,p)

binomial distribution

f (k) = nCk pk(1-p)n-k

Poisson(λ)

Poisson distribution

f (k) = λke-λ / k!

Geom(p)

geometric distribution

f (k) = p(1-p) k

HG(N,K,n)

hyper-geometric distribution

 

Bern(p)

Bernoulli distribution

 




Frequently Asked Questions:

 

1. What is the significance of (P) in probability symbols?

  The symbol (P) in probability notation represents the probability function, indicating the likelihood of an event occurring. It is a fundamental element in probability theory.

 2. Can you explain the concept of conditional probability (P(A | B))?

  Conditional probability (P(A | B)) is the probability of event A occurring given that event B has occurred. It is calculated by dividing the probability of the intersection of A and B by the probability of B.

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