====== PROBABILITY AND STATISTICS ======


^ MANTRAKSHAR	^	HINDI	^	Symbol Name	^	Meaning / definition	^	Example	^
|	P(A)	|	 प्रायिकता या संभाव्यता फलन 	|	probability function	|	probability of event A	|	P(A) = 0.5	|
|	P(A ⋂ B)	|		|	probability of events intersection	|	probability that of events A and B	|	P(A⋂B) = 0.5	|
|	P(A ⋃ B)	|		|	probability of events union	|	probability that of events A or B	|	P(A⋃B) = 0.5	|
|	{P(A vert B)}	|		|	conditional probability function	|	probability of event A given event B occured	|	P(A . B) = 0.3	|
|	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	|	आबादी माध्य 	|	population mean	|	mean of population values	|	μ = 10	|
|	E(X)	|		|	expectation value	|	expected value of random variable X	|	E(X) = 10	|
|	E(X｜Y)	|		|	conditional expectation	|	expected value of random variable X given Y	|	E(X ｜Y=2) = 5	|
|	var(X)	|	प्रसरण	|	variance	|	variance of random variable X	|	var(X) = 4	|
|	σ2	|	प्रसरण	|	variance	|	variance of population values	|	σ2 = 4	|
|	std(X)	|	मानक विचलन	|	standard deviation	|	standard deviation of random variable X	|	std(X) = 2	|
|	σX	|	मानक विचलन	|	standard deviation	|	standard deviation value of random variable X	|	σX  = 2	|
|		|		|	median	|	middle value of random variable x	|		|
|	cov(X,Y)	|	सहप्रसरण	|	covariance	|	covariance of random variables X and Y	|	cov(X,Y) = 4	|
|	corr(X,Y)	|		|	correlation	|	correlation of random variables X and Y	|	corr(X,Y) = 0.6	|
|	ρX,Y	|		|	correlation	|	correlation of random variables X and Y	|	ρX,Y = 0.6	|
|	∑	|	संकलन	|	summation	|	summation - sum of all values in range of series	|		|
|	∑∑	|		|	double summation	|	double summation	|		|
|	Mo	|	बहुलक	|	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	|	x = (2+5+9) / 3 = 5.333	|
|	s 2	|		|	sample variance	|	population samples variance estimator	|	s 2 = 4	|
|	s	|		|	sample standard deviation	|	population samples standard deviation estimator	|	s = 2	|
|	zx	|		|	standard score	|	zx = (x-x) / sx	|		|
|	X ~	|		|	distribution of X	|	distribution of random variable X	|	X ~ N(0,3)	|
|	N(μ,σ2)	|	प्रसामान्य बंटन	|	normal distribution	|	gaussian distribution	|	X ~ N(0,3)	|
|	U(a,b)	|		|	uniform distribution	|	equal probability in range a,b 	|	X ~ U(0,3)	|
|	exp(λ)	|		|	exponential distribution	|	f (x) = λe-λx , x≥0	|		|
|	gamma(c, λ)	|		|	gamma distribution	|	f (x) = λ c xc-1e-λx / Γ©, 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	|		|		|