Single Event Probability Formula :

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

Multiple Event Probability Formula :

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

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Formulas:

Sensitivity = TP / ( TP + FN )
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,
TP = True Positive.
FP = False Positive.
FN = False Negative.
TN = True Negative

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Formula

Standard Deviation Confidence Interval for Variance = [(n-1)×S² / χ²_{α/2, n-1}] ≤ σ² ≤ [(n-1)×S² / χ²_{1-α/2, n-1}]


Where,
n = Sample Size
S = Variance
α = 1 - (Confidence Level/100)
χ²_{α/2, n-1} = χ²-table value

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Formula Used:
pdf =

Where,
pdf - Probability Density Function
Β - Beta Function
x - Probability Distribution Intervals (0≤x≤1)
α and β - Positive shape parameters

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Formula Used:



Where,
is the mean,
s is the Standard Deviation,
N is the number of data points.

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Formula:
Harmonic mean =
where,
d is the data values and
f is the corresponding frequency values.

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

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Formula:

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,

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Formula:
C^R(n,r) = C(n+r-1,r) = (n+r-1)! / r! (n - 1)! For n >= 0, and r >= 0.

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Formula:
P^R(n,r) = n^rFor, n >= 0, and r >= 0.

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Formula:
nP_r=n^r

Where,
n is the number of types,
r is the number (of times) to be chosen.

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Formula:


Where,
n is the number of types,
r is the number (of times) to be chosen.

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Formula:

Lower Limit = m - t_0.975,n-1 x √((n+1)/n) x s.d
Upper Limit = m + t_0.975,n-1 x √((n+1)/n) x s.d
SDSRRL = s.d / 2
LlciLlrr = Llrr - t_0.975,n-1 x √((n+1)/n) x SDSRRL
UlciLlrr = Llrr + t_0.975,n-1 x √((n+1)/n) x SDSRRL
LlciUlrr = Ulrr - t_0.975,n-1 x √((n+1)/n) x SDSRRL
UlciUlrr = Ulrr + t_0.975,n-1 x √((n+1)/n) x SDSRRL


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

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Formula:

M = C x E


Where,
C = Critical Value
E = Standard Error of the Statistics
M = Margin of Error

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Formula :
Probability P(X-μ<2σ) = 1 - (1/K²)

Where,
K = Standard Deviation

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Formula:
P (X = r) = _nC_r p^r (1-p)^n-r


Where,

Combination _nC_r = n! / ((n- r)! × r!)
n = number of events
p = Probability of success for each trial
r = 0, 1, ... n

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