Returned 93 matches (100 formulae, 80 docs)
    Lookup 11.889 ms, Re-ranking 0.154 ms
    Found 149682 tuple postings, 83810 formulae, 16394 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Statistical_coupling_analysis.html
P i x = N ! n x ! ( N - n x ) ! p x n x ( 1 - p x ) N - n x

Doc 2
0.3154
0.3154
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Multiplicity_function_for_N_noninteracting_spins.html
W ( n , N ) = ( N n ) = N ! n ! ( N - n ) !

Doc 3
0.2932
0.2932
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Freshman's_dream.html
( p n ) = p ! n ! ( p - n ) ! .

Doc 4
0.2867
0.4183
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Rule_of_succession.html
f ( p ) = ( n + 1 ) ! s ! ( n - s ) ! p s ( 1 - p ) n - s .
1 p ( 1 - p )

Doc 5
0.2734
0.4800
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Poisson_limit_theorem.html
p n ( k ) = n ! ( n - k ) ! k ! p k ( 1 - p ) n - k .
n ! ( n - k ) ! k ! p k ( 1 - p ) n - k e - λ λ k k ! .

Doc 6
0.2469
0.2469
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/An_Essay_towards_solving_a_Problem_in_the_Doctrine_of_Chances.html
f ( p ) = ( n + 1 ) ! k ! ( n - k ) ! p k ( 1 - p ) n - k for 0 p 1

Doc 7
0.2353
0.2353
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Brownian_motion.html
( N N R ) = N ! N R ! ( N - N R ) !

Doc 8
0.2330
0.2330
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Langmuir_adsorption_model.html
Ω c o n f = N S ! N ! ( N S - N ) !

Doc 9
0.2295
0.2295
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Fermi–Dirac_statistics.html
w ( n i , g i ) = g i ! n i ! ( g i - n i ) ! .

Doc 10
0.2061
0.7263
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Taylor's_law.html
s 2 = n p ( 1 - p )
s 2 = n p ( 1 - p )
s 2 = a p b ( 1 - p ) c
D = v a r o b s v a r b i n = s 2 n p ( 1 - p )

Doc 11
0.2021
0.2021
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Inclusion–exclusion_principle.html
( n p ) = n ! p ! ( n - p ) !

Doc 12
0.2000
0.2000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Ramsey's_theorem.html
| C k | c k ! n ! ( k - n ) !

Doc 13
0.1921
0.1921
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Einstein_solid.html
Ω = ( q + N - 1 ) ! q ! ( N - 1 ) !

Doc 14
0.1889
1.0646
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_distribution.html
Var [ X ] = n p ( 1 - p ) .
( n k ) = n ! k ! ( n - k ) !
1 - 6 p ( 1 - p ) n p ( 1 - p )
X - n p n p ( 1 - p )
𝒩 ( n p , n p ( 1 - p ) ) ,
f ( k ; n , p ) = Pr ( X = k ) = ( n k ) p k ( 1 - p ) n - k
g n ( p ) = n p ( 1 - p )

Doc 15
0.1809
0.3150
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_theorem.html
( n k ) = n ! k ! ( n - k ) !
n ! k ! ( n - k ) !

Doc 16
0.1809
0.1809
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Bézier_curve.html
( n i ) = n ! i ! ( n - i ) !

Doc 17
0.1809
0.1809
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pascal's_triangle.html
( n r ) = n ! r ! ( n - r ) !

Doc 18
0.1809
0.1809
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bézier_surface.html
( n i ) = n ! i ! ( n - i ) !

Doc 19
0.1809
0.1809
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Lottery_mathematics.html
( n k ) = n ! k ! ( n - k ) !

Doc 20
0.1809
0.1809
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/General_Leibniz_rule.html
( n k ) = n ! k ! ( n - k ) !

Doc 21
0.1809
0.1809
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Hypercube.html
( n m ) = n ! m ! ( n - m ) !

Doc 22
0.1803
0.5566
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bose–Einstein_statistics.html
w ( n , g ) = ( n + g - 1 ) ! n ! ( g - 1 ) ! .
w ( n , 2 ) = ( n + 1 ) ! n ! 1 ! .
k = 0 n ( k + a ) ! k ! a ! = ( n + a + 1 ) ! n ! ( a + 1 ) ! .
k = 0 n ( k + a ) ! k ! a ! = ( n + a + 1 ) ! n ! ( a + 1 ) ! .

Doc 23
0.1780
0.3122
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Combination.html
( n k ) = n ! k ! ( n - k ) ! ,
n ! k ! ( n - k ) !

Doc 24
0.1780
0.1780
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Cake_number.html
( n k ) = n ! k ! ( n - k ) ! ,

Doc 25
0.1780
0.1780
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Mashreghi–Ransford_inequality.html
( n k ) = n ! k ! ( n - k ) ! .

Doc 26
0.1780
0.1780
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Gamma_function.html
( n k ) = n ! k ! ( n - k ) ! .

Doc 27
0.1780
0.1780
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Recurrence_relation.html
( n k ) = n ! k ! ( n - k ) ! .

Doc 28
0.1780
0.1780
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Proofs_of_Fermat's_little_theorem.html
( n i ) = n ! i ! ( n - i ) ! ,

Doc 29
0.1775
0.1775
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Quantile_function.html
α = 4 p ( 1 - p ) .

Doc 30
0.1746
0.1746
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Quantum_finance.html
C 0 N = ( 1 + r ) - N n = 0 N N ! n ! ( N - n ) ! q n ( 1 - q ) N - n [ S 0 ( 1 + b ) n ( 1 + a ) N - n - K ] +

Doc 31
0.1744
0.1744
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Natural_exponential_family.html
V a r ( X ) = n p ( 1 - p )

Doc 32
0.1734
0.1734
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kelly_criterion.html
2 N p K ( 1 - p ) N - K W .

Doc 33
0.1726
0.1726
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Multinomial_distribution.html
var ( X i ) = n p i ( 1 - p i ) .

Doc 34
0.1722
0.2999
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Maximum_entropy_probability_distribution.html
f ( k ) = ( n k ) p k ( 1 - p ) n - k
f ( k ) = p k ( 1 - p ) 1 - k

Doc 35
0.1720
0.4738
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/(a,b,0)_class_of_distributions.html
Γ ( r + k ) k ! Γ ( r ) p r ( 1 - p ) k
n p ( 1 - p )
( n k ) p k ( 1 - p ) n - k
Doc 36
0.1683
0.3283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Bose–Hubbard_model.html
D f = L ! N f ! ( L - N f ) ! .
D b = ( N b + L - 1 ) ! N b ! ( L - 1 ) !

Doc 37
0.1674
0.1674
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Variance.html
p ( k ) = ( n k ) p k ( 1 - p ) n - k ,

Doc 38
0.1667
0.1667
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Gibbs_paradox.html
( N n A ) = N ! n A ! n B !

Doc 39
0.1603
0.5632
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_process.html
P ( [ ω 1 , ω 2 , , ω n ] ) = p k ( 1 - p ) n - k
N ( k , n ) = ( n k ) = n ! k ! ( n - k ) !
P ( X 1 = ω 1 , X 2 = ω 2 , , X n = ω n ) = p k ( 1 - p ) n - k
E [ X i = H k out of n times ] = P ( k , n ) = ( n k ) p k ( 1 - p ) n - k

Doc 40
0.1596
0.2998
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Theoretical_ecology.html
d p d t = m p ( 1 - p ) - e p
d p 1 d t = m 1 p 1 ( 1 - p 1 ) - e p 1

Doc 41
0.1589
0.1589
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Concentration_inequality.html
n p ( 1 - p )

Doc 42
0.1586
0.1586
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Binomial_sum_variance_inequality.html
Var ( Z ) = n p ¯ ( 1 - p ¯ ) - n s 2 ,

Doc 43
0.1538
0.4327
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Binomial_proportion_confidence_interval.html
p ^ ± z 1 n p ^ ( 1 - p ^ )
p ~ ± z 1 n ~ p ~ ( 1 - p ~ )
v a r ( p ) = p ( 1 - p ) n
Doc 44
0.1529
0.1529
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Median.html
p ( 1 - p ) n f ( x p ) 2

Doc 45
0.1509
0.1509
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Sequential_decoding.html
p d i ( 1 - p ) n i b - d i 2 - ( N - n i ) b

Doc 46
0.1478
0.5619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
( n k ) = n ! k ! ( n - k ) ! for 0 k n ,
( n k ) p k ( 1 - p ) n - k .
n p , n p ( 1 - p )
n ! k ! ( n - k ) !

Doc 47
0.1469
0.1469
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degree_distribution.html
P ( k ) = ( n - 1 k ) p k ( 1 - p ) n - 1 - k ,

Doc 48
0.1463
0.2788
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Mean_absolute_difference.html
E ( R ( S ) ) = i = 0 n p i ( 1 - p ) n - i r i ,
p ( 1 - p )

Doc 49
0.1455
0.2834
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Erdős–Rényi_model.html
p M ( 1 - p ) ( n 2 ) - M .
P ( deg ( v ) = k ) = ( n - 1 k ) p k ( 1 - p ) n - 1 - k ,

Doc 50
0.1449
0.1449
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Principle_of_maximum_entropy.html
W = N ! n 1 ! n 2 ! n m !

Doc 51
0.1447
0.4156
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Odds_ratio.html
p x ( 1 - p y )
( 1 - p x ) ( 1 - p y )
( 1 - p x ) p y
Doc 52
0.1441
0.1441
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Term_symbol.html
N = ( t e ) = t ! e ! ( t - e ) ! .

Doc 53
0.1429
0.1429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bean_machine.html
( n k ) p k ( 1 - p ) n - k

Doc 54
0.1413
0.2757
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Order_statistic.html
n ! ( k - 1 ) ! ( n - k ) ! u k - 1 ( 1 - u ) n - k d u + O ( d u 2 ) ,
f X ( k ) ( x ) = n ! ( k - 1 ) ! ( n - k ) ! [ F X ( x ) ] k - 1 [ 1 - F X ( x ) ] n - k f X ( x )

Doc 55
0.1412
0.1412
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Network_science.html
P ( deg ( v ) = k ) = ( n - 1 k ) p k ( 1 - p ) n - 1 - k

Doc 56
0.1412
0.1412
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Score_(statistics).html
L ( θ ; A , B ) = ( A + B ) ! A ! B ! θ A ( 1 - θ ) B ,

Doc 57
0.1387
0.1387
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Step-growth_polymerization.html
N x N = ( 1 - p ) p x - 1

Doc 58
0.1379
0.1379
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
( n n ) = n ! n ! 0 ! = 1

Doc 59
0.1348
0.1348
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Bit_error_rate.html
p p = 1 - ( 1 - p e ) N

Doc 60
0.1342
0.1342
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Likelihood_principle.html
p 3 ( 1 - p ) 9

Doc 61
0.1341
0.1341
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Field_with_one_element.html
n ! m ! ( n - m ) !

Doc 62
0.1341
0.1341
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Kummer's_theorem.html
n ! m ! ( n - m ) !

Doc 63
0.1340
0.1340
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Effective_population_size.html
N e ( v ) = p ( 1 - p ) 2 var ^ ( p ) .

Doc 64
0.1333
0.1333
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Rook_polynomial.html
( 64 8 ) = 64 ! 8 ! ( 64 - 8 ) ! = 4 , 426 , 165 , 368.

Doc 65
0.1325
0.1325
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Balding–Nichols_model.html
F p ( 1 - p )

Doc 66
0.1325
0.1325
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Wahlund_effect.html
2 p ( 1 - p )

Doc 67
0.1325
0.1325
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Fixation_index.html
2 p ( 1 - p )

Doc 68
0.1316
0.2566
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Credit_default_swap.html
p 1 ( 1 - p 2 )
p 1 p 2 ( 1 - p 3 )

Doc 69
0.1316
0.1316
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_distribution.html
1 p ( 1 - p )

Doc 70
0.1310
0.1310
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Beverton–Holt_model.html
n t = K n 0 n 0 + ( K - n 0 ) R 0 - t .

Doc 71
0.1306
0.1306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Incomplete_information_network_game.html
\Q ( k ; p ) = ( N - 2 k - 1 ) p ( k - 1 ) ( 1 - p ) ( N - k - 1 )

Doc 72
0.1299
0.1299
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Template:Negative_binomial_distribution.html
r p 2 ( 1 - p )

Doc 73
0.1266
0.2532
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Beta_distribution.html
1 p ( 1 - p )
1 p ( 1 - p )

Doc 74
0.1266
0.1266
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Hypergeometric_distribution.html
1 n K ( N - K ) ( N - n ) ( N - 2 ) ( N - 3 )

Doc 75
0.1257
0.1257
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Yule–Simon_distribution.html
g ( k ; p ) = p ( 1 - p ) k - 1

Doc 76
0.1250
0.1250
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Margin_of_error.html
Standard error p ( 1 - p ) n

Doc 77
0.1243
0.2467
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Checking_whether_a_coin_is_fair.html
s p = p ( 1 - p ) n
f ( r | H = h , T = t ) = ( h + t + 1 ) ! h ! t ! r h ( 1 - r ) t .

Doc 78
0.1240
0.1240
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Return_period.html
n ! ( n - r ) ! r ! μ r ( 1 - μ ) n - r e - λ λ r r ! .

Doc 79
0.1229
0.1229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/F-statistics.html
F S T = var ( 𝐩 ) p ( 1 - p )

Doc 80
0.1220
0.1220
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Proportional_approval_voting.html
c ! s ! ( c - s ) !