Probability of event A that does not occur P(A') = 1 - P(A).

P(A') = 1 - P(A).

P(B) = n(B) / n(S).

P(B') = 1 - P(B).

Probability that both the events occur P(A ∩ B) = P(A) x P(B).

Probability that either of event occurs P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Conditional Probability P(A | B) = P(A ∩ B) / P(B).

Where,

n(A) - Number of Occurrence in Event A,

n(B) - Number of Occurrence in Event B,

n(S) - Total Number of Possible Outcomes.

Specificity = TN / ( FP + TN )

Predictive Value Positive = TP / ( TP + FP )

Predictive Value Negative = TN / ( FN + TN )

Positive Likelihood = Sensitivity / ( 1 - Specificity )

Negative Likelihood = ( 1 - Sensitivity ) / Specificity

Where,

Standard Deviation Confidence Interval for Variance = [(n-1)×S² / χ²

Where,

n = Sample Size

S = Variance

α = 1 - (Confidence Level/100)

χ²

Where,

Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX

Intercept(a) = (ΣY - b(ΣX)) / N

pdf =

Where,

pdf - Probability Density Function

Β - Beta Function

x - Probability Distribution Intervals (0≤x≤1)

α and β - Positive shape parameters

Where,

is the mean,

s is the Standard Deviation,

N is the number of data points.

Harmonic mean =

where,

d is the data values and

f is the corresponding frequency values.

Circular Permutation (Pn) = (n-1)!

Relative Risk (RR) = ( a / ( a + b ) ) / ( c / ( c + d ) )

Where,

a = Exposed Group Positive Outcome,

b = Exposed Group Negative Outcome,

c = Control Group Positive Outcome,

d = Control Group Negative Outcome,

C

P

Odd Permutation = n! / 2 ∀ n>=2

Even Permutation = n! / 2 ∀ n>2

nP

Where,

n is the number of types,

r is the number (of times) to be chosen.

Where,

n is the number of types,

r is the number (of times) to be chosen.

Lower Limit = m - t

Upper Limit = m + t

SDSRRL = s.d / 2

LlciLlrr = Llrr - t

UlciLlrr = Llrr + t

LlciUlrr = Ulrr - t

UlciUlrr = Ulrr + t

Where,

t - Distribution.

s.d - Standard Deviation

n - Total Count

m - Mean

LlciLlrr - is the Lower limit of the confidence interval of the Lower limit of the standard reference range

UlciLlrr - is the Upper limit of the confidence interval of the Lower limit of the standard reference range

LlciUlrr - is the Lower limit of the confidence interval of the Upper limit of the standard reference range

UlciUlrr - is the Upper limit of the confidence interval of the Upper limit of the standard reference range

SDSRRL - is the standard deviation of the standard reference range limit

Llrr - is the Lower limit of the standard reference range

Ulrr - is the Upper limit of the standard reference range

Where,

C = Critical Value

E = Standard Error of the Statistics

M = Margin of Error

Probability P(X-μ<2σ) = 1 - (1/K

Where,

K = Standard Deviation

Where,

X,Y - set of values

α , β - constant values

n - Set value counts

P (X = r) =

Where,

Combination _{n}C_{r} = n! / ((n- r)! × r!)

n = number of events

p = Probability of success for each trial

r = 0, 1, ... n

Mean = Sum of data values / N(Number of Values)

Where,

n

s

k=Number of group

M=Mean

Where,

n = Number of Persons in a Group

p(n) = Probability with Same Birthdays