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## Probability Symbols

### 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

#### 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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