maths.Statistical Symbols

Question 1

P(A)

Answer 1

probability function.

P(A)
👉  probability of event A 

P(A)

Question 2

P(A ∩ B)

Answer 2

probability of events intersection.

P(A ∩ B)
👉 probability that of events A and B    

P(A ∩ B)

Question 3

P(A ∪ B)

Answer 3

probability of events union.

P(A ∪ B)
probability that of events A or B.

P(A ∪ B)

Question 4

P(A | B)

Answer 4

conditional probability function.

P(A | B)
probability of event A if event B occured.

Question 5

f(x)

Answer 5

probability density function (pdf) — defines the relationship between a random variable and its probability.

P(a ≤ x ≤ b) = ∫ f (x) dx

Question 6

F(x)

Answer 6

cumulative distribution function(cdf) — gives the probability that the random variable X is less than or equal to x

F(x) = P(X≤ x)  

Question 7

μ

Answer 7

population mean (average).

Question 8

E(X)

Answer 8

expected value of random variable X - означающее среднее значение случайной величины. В случае непрерывной случайной величины подразумевается взвешивание по плотности распределения.

Question 9

E(X | Y)

Answer 9

conditional expectation - expected value of random variable X given Y.

Question 10

var(X)

Answer 10

variance of random variable X.

Question 11

σ2

Answer 11

variance of population values.

Question 12

σ

Answer 12

standard deviation.

Question 13

std(X)

Answer 13

standard deviation of random variable X.

Question 14

x̄(median)

Answer 14

middle value of random variable x

Question 15

cov(X,Y)

Answer 15

covariance(мера зависимости двух случайных величин) of random variables X and Y

Question 16

corr(X,Y)

Answer 16

correlation of random variables X and Y

Question 17

ρX,Y

Answer 17

correlation of random variables X and Y

Question 18

∑

Answer 18

summation of all values in range of series

Question 19

Mo

Answer 19

mode. Value that occurs most frequently in population.

Question 20

MR

Answer 20

mid-range

MR = (xmax + xmin) / 2

Question 21

Md

Answer 21

sample median. Half the population is below this value

Question 22

Q1

Answer 22

lower / first quartile. 25% of population are below this value.

Question 23

Q2

Answer 23

median / second quartile. 50% of popul are below this value=median of sampl

Question 24

x̄

Answer 24

sample mean. Average / arithmetic mean

Question 25

s2

Answer 25

sample variance. Population samples variance estimator.

Question 26

s

Answer 26

sample standard deviation. Population samples standard deviation estimator

Question 27

zx

Answer 27

standard score.

zx = (x-x) / sx 

Question 28

X~

Answer 28

distribution of random variable X 👉 X ~ N(0,3). Describes how values are distributed for a field, shows which values are common and uncommon.

Question 29

N(μ,σ2)

Answer 29

normal distribution or gaussian distribution

X ~ N(0,3)

Question 30

U(a,b)

Answer 30

Uniform distribution — simplest probability distribution, very useful in modeling random variables. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur.

Question 31

exp(λ)

Answer 31

Exponential distribution — continuous probability distribution that often concerns the amount of time until some specific event happens. It is a process in which events happen continuously and independently at a constant average rate.

f (x) = λe-λx , x≥0

Question 32

β(Beta)

Answer 32

The probability of Type II error(false negative) in a statistical hypothesis test.

Question 33

gamma(c, λ)

Answer 33

Gamma distribution is a kind of statistical distributions which is related to the beta distribution. This distribution arises naturally in which the waiting time between Poisson distributed events are relevant to each other.

Question 34

F(k1, k2)

Answer 34

F distribution

Question 35

Bin(n,p)

Answer 35

Биномиа́льное распределе́ние с параметрами n и p в теории вероятностей — распределение количества «успехов» в последовательности из n независимых случайных экспериментов, таких, что вероятность «успеха» в каждом из них постоянна и равна p.

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

Question 36

Poisson(λ)

Answer 36

The Poisson distribution is a discrete distribution that measures the probability of a given number of events happening in a specified time period.

f (k) = λke-λ / k!

Question 37

Geom(p)

Answer 37

geometric distribution is defined as a discrete probability distribution of a random variable “x” which satisfies some of the conditions and has a series of trials. Each trial has only two possible outcomes – either success or failure.

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

Question 38

n!

Answer 38

factorial

n! = 1⋅2⋅3⋅...⋅n 👉 5! = 1⋅2⋅3⋅4⋅5 = 120

Question 39

n!

Answer 39

factorial

n! = 1⋅2⋅3⋅...⋅n 👉 5! = 1⋅2⋅3⋅4⋅5 = 120

Question 40

nPk

Answer 40

permutation

5P3 = 5! / (5-3)! = 60