tangent
Not Supported
P
i
x
=
N
!
n
x
!
(
N
-
n
x
)
!
p
x
n
x
(
1
-
p
x
)
N
-
n
x
Search
Returned 90 matches (100 formulae, 80 docs)
Lookup 11.889 ms, Re-ranking 1336.288 ms
Found 149682 tuple postings, 83810 formulae, 16394 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
P
i
x
=
N
!
n
x
!
(
N
-
n
x
)
!
p
x
n
x
(
1
-
p
x
)
N
-
n
x
Doc 1
1.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Statistical_coupling_analysis.html
W
(
n
,
N
)
=
(
N
n
)
=
N
!
n
!
(
N
-
n
)
!
Doc 2
0.3210, 0.3210
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Multiplicity_function_for_N_noninteracting_spins.html
(
p
n
)
=
p
!
n
!
(
p
-
n
)
!
.
Doc 3
0.3005, 0.3005
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Freshman's_dream.html
f
(
p
)
=
(
n
+
1
)
!
s
!
(
n
-
s
)
!
p
s
(
1
-
p
)
n
-
s
.
Doc 4
0.2918, 0.4347
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Rule_of_succession.html
p
n
(
k
)
=
n
!
(
n
-
k
)
!
k
!
p
k
(
1
-
p
)
n
-
k
.
Doc 5
0.2558, 0.4443
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Poisson_limit_theorem.html
f
(
p
)
=
(
n
+
1
)
!
k
!
(
n
-
k
)
!
p
k
(
1
-
p
)
n
-
k
for
0
≤
p
≤
1
Doc 6
0.2515, 0.2515
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/An_Essay_towards_solving_a_Problem_in_the_Doctrine_of_Chances.html
(
N
N
R
)
=
N
!
N
R
!
(
N
-
N
R
)
!
Doc 7
0.2427, 0.2427
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Brownian_motion.html
Ω
c
o
n
f
=
N
S
!
N
!
(
N
S
-
N
)
!
Doc 8
0.2404, 0.2404
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Langmuir_adsorption_model.html
w
(
n
i
,
g
i
)
=
g
i
!
n
i
!
(
g
i
-
n
i
)
!
.
Doc 9
0.2358, 0.2358
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Fermi–Dirac_statistics.html
|
C
k
|
≤
c
k
!
n
!
(
k
-
n
)
!
Doc 10
0.2079, 0.2079
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Ramsey's_theorem.html
s
2
=
n
p
(
1
-
p
)
Doc 11
0.1916, 0.6465
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Taylor's_law.html
Doc 11
0.1916, 0.6465
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Taylor's_law.html
Ω
=
(
q
+
N
′
-
1
)
!
q
!
(
N
′
-
1
)
!
Doc 12
0.1905, 0.1905
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Einstein_solid.html
n
!
(
n
-
k
)
!
k
!
p
k
(
1
-
p
)
n
-
k
→
e
-
λ
λ
k
k
!
.
Doc 5
0.2558, 0.4443
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Poisson_limit_theorem.html
α
=
4
p
(
1
-
p
)
.
Doc 13
0.1871, 0.1871
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Quantile_function.html
w
(
n
,
g
)
=
(
n
+
g
-
1
)
!
n
!
(
g
-
1
)
!
.
Doc 14
0.1870, 0.5747
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bose–Einstein_statistics.html
2
N
p
K
(
1
-
p
)
N
-
K
W
.
Doc 15
0.1829, 0.1829
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kelly_criterion.html
s
2
=
a
p
b
(
1
-
p
)
c
Doc 11
0.1916, 0.6465
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Taylor's_law.html
Γ
(
r
+
k
)
k
!
Γ
(
r
)
p
r
(
1
-
p
)
k
Doc 16
0.1809, 0.4776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/(a,b,0)_class_of_distributions.html
f
(
k
)
=
(
n
k
)
p
k
(
1
-
p
)
n
-
k
Doc 17
0.1801, 0.3169
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Maximum_entropy_probability_distribution.html
(
n
m
)
=
n
!
m
!
(
n
-
m
)
!
Doc 26
0.1789, 0.1789
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Hypercube.html
(
n
p
)
=
n
!
p
!
(
n
-
p
)
!
Doc 25
0.1789, 0.1789
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Inclusion–exclusion_principle.html
(
n
k
)
=
n
!
k
!
(
n
-
k
)
!
Doc 18
0.1789, 0.9645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_distribution.html
Doc 19
0.1789, 0.3115
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_theorem.html
Doc 20
0.1789, 0.1789
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Lottery_mathematics.html
Doc 24
0.1789, 0.1789
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/General_Leibniz_rule.html
(
n
r
)
=
n
!
r
!
(
n
-
r
)
!
Doc 22
0.1789, 0.1789
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pascal's_triangle.html
(
n
i
)
=
n
!
i
!
(
n
-
i
)
!
Doc 21
0.1789, 0.1789
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Bézier_curve.html
Doc 23
0.1789, 0.1789
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bézier_surface.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 27
0.1779, 0.1779
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Quantum_finance.html
(
n
k
)
=
n
!
k
!
(
n
-
k
)
!
,
Doc 28
0.1762, 0.3087
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Combination.html
Doc 31
0.1762, 0.1762
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Cake_number.html
(
n
k
)
=
n
!
k
!
(
n
-
k
)
!
.
Doc 29
0.1762, 0.1762
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Recurrence_relation.html
Doc 30
0.1762, 0.1762
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Mashreghi–Ransford_inequality.html
Doc 33
0.1762, 0.1762
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Gamma_function.html
(
n
i
)
=
n
!
i
!
(
n
-
i
)
!
,
Doc 32
0.1762, 0.1762
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Proofs_of_Fermat's_little_theorem.html
Var
[
X
]
=
n
p
(
1
-
p
)
.
Doc 18
0.1789, 0.9645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_distribution.html
(
N
n
A
)
=
N
!
n
A
!
n
B
!
Doc 34
0.1758, 0.1758
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Gibbs_paradox.html
p
(
k
)
=
(
n
k
)
p
k
(
1
-
p
)
n
-
k
,
Doc 35
0.1751, 0.1751
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Variance.html
d
p
d
t
=
m
p
(
1
-
p
)
-
e
p
Doc 36
0.1684, 0.3166
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Theoretical_ecology.html
D
f
=
L
!
N
f
!
(
L
-
N
f
)
!
.
Doc 37
0.1667, 0.3164
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Bose–Hubbard_model.html
V
a
r
(
X
)
=
n
p
(
1
-
p
)
Doc 38
0.1624, 0.1624
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Natural_exponential_family.html
p
^
±
z
1
n
p
^
(
1
-
p
^
)
Doc 39
0.1619, 0.4277
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Binomial_proportion_confidence_interval.html
var
(
X
i
)
=
n
p
i
(
1
-
p
i
)
.
Doc 40
0.1608, 0.1608
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Multinomial_distribution.html
P
(
[
ω
1
,
ω
2
,
⋯
,
ω
n
]
)
=
p
k
(
1
-
p
)
n
-
k
Doc 41
0.1590, 0.5657
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_process.html
p
~
±
z
1
n
~
p
~
(
1
-
p
~
)
Doc 39
0.1619, 0.4277
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Binomial_proportion_confidence_interval.html
p
x
(
1
-
p
y
)
Doc 42
0.1558, 0.4365
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Odds_ratio.html
p
M
(
1
-
p
)
(
n
2
)
-
M
.
Doc 43
0.1557, 0.3002
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Erdős–Rényi_model.html
P
(
k
)
=
(
n
-
1
k
)
p
k
(
1
-
p
)
n
-
1
-
k
,
Doc 44
0.1538, 0.1538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degree_distribution.html
E
(
R
(
S
)
)
=
∑
i
=
0
n
p
i
(
1
-
p
)
n
-
i
r
i
,
Doc 45
0.1532, 0.2970
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Mean_absolute_difference.html
W
=
N
!
n
1
!
n
2
!
⋯
n
m
!
Doc 46
0.1531, 0.1531
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Principle_of_maximum_entropy.html
(
n
k
)
p
k
(
1
-
p
)
n
-
k
Doc 16
0.1809, 0.4776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/(a,b,0)_class_of_distributions.html
Doc 47
0.1529, 0.1529
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bean_machine.html
N
=
(
t
e
)
=
t
!
e
!
(
t
-
e
)
!
.
Doc 48
0.1518, 0.1518
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Term_symbol.html
(
n
k
)
p
k
(
1
-
p
)
n
-
k
.
Doc 49
0.1503, 0.5558
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
D
b
=
(
N
b
+
L
-
1
)
!
N
b
!
(
L
-
1
)
!
Doc 37
0.1667, 0.3164
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Bose–Hubbard_model.html
d
p
1
d
t
=
m
1
p
1
(
1
-
p
1
)
-
e
p
1
Doc 36
0.1684, 0.3166
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Theoretical_ecology.html
P
(
deg
(
v
)
=
k
)
=
(
n
-
1
k
)
p
k
(
1
-
p
)
n
-
1
-
k
Doc 50
0.1479, 0.1479
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Network_science.html
(
n
n
)
=
n
!
n
!
0
!
=
1
Doc 51
0.1477, 0.1477
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
(
n
k
)
=
n
!
k
!
(
n
-
k
)
!
for
0
≤
k
≤
n
,
Doc 49
0.1503, 0.5558
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
(
1
-
p
x
)
p
y
Doc 42
0.1558, 0.4365
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Odds_ratio.html
p
3
(
1
-
p
)
9
Doc 52
0.1457, 0.1457
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Likelihood_principle.html
P
(
deg
(
v
)
=
k
)
=
(
n
-
1
k
)
p
k
(
1
-
p
)
n
-
1
-
k
,
Doc 43
0.1557, 0.3002
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Erdős–Rényi_model.html
p
p
=
1
-
(
1
-
p
e
)
N
Doc 53
0.1444, 0.1444
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Bit_error_rate.html
p
(
1
-
p
)
Doc 45
0.1532, 0.2970
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Mean_absolute_difference.html
2
p
(
1
-
p
)
Doc 56
0.1438, 0.1438
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Wahlund_effect.html
Doc 57
0.1438, 0.1438
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Fixation_index.html
F
p
(
1
-
p
)
Doc 54
0.1438, 0.1438
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Balding–Nichols_model.html
n
p
(
1
-
p
)
Doc 16
0.1809, 0.4776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/(a,b,0)_class_of_distributions.html
Doc 55
0.1438, 0.1438
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Concentration_inequality.html
p
1
(
1
-
p
2
)
Doc 58
0.1429, 0.2787
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Credit_default_swap.html
1
p
(
1
-
p
)
Doc 4
0.2918, 0.4347
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Rule_of_succession.html
Doc 59
0.1429, 0.1429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_distribution.html
r
p
2
(
1
-
p
)
Doc 60
0.1410, 0.1410
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Template:Negative_binomial_distribution.html
(
64
8
)
=
64
!
8
!
(
64
-
8
)
!
=
4
,
426
,
165
,
368.
Doc 61
0.1405, 0.1405
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Rook_polynomial.html
n
!
(
k
-
1
)
!
(
n
-
k
)
!
u
k
-
1
(
1
-
u
)
n
-
k
d
u
+
O
(
d
u
2
)
,
Doc 62
0.1402, 0.2686
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Order_statistic.html
L
(
θ
;
A
,
B
)
=
(
A
+
B
)
!
A
!
B
!
θ
A
(
1
-
θ
)
B
,
Doc 63
0.1401, 0.1401
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Score_(statistics).html
N
(
k
,
n
)
=
(
n
k
)
=
n
!
k
!
(
n
-
k
)
!
Doc 41
0.1590, 0.5657
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_process.html
Var
(
Z
)
=
n
p
¯
(
1
-
p
¯
)
-
n
s
2
,
Doc 64
0.1397, 0.1397
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Binomial_sum_variance_inequality.html
n
t
=
K
n
0
n
0
+
(
K
-
n
0
)
R
0
-
t
.
Doc 65
0.1385, 0.1385
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Beverton–Holt_model.html
1
p
(
1
-
p
)
Doc 66
0.1375, 0.2750
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Beta_distribution.html
Doc 66
0.1375, 0.2750
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Beta_distribution.html
N
x
N
=
(
1
-
p
)
p
x
-
1
Doc 67
0.1371, 0.1371
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Step-growth_polymerization.html
f
(
k
)
=
p
k
(
1
-
p
)
1
-
k
Doc 17
0.1801, 0.3169
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Maximum_entropy_probability_distribution.html
P
(
X
1
=
ω
1
,
X
2
=
ω
2
,
⋯
,
X
n
=
ω
n
)
=
p
k
(
1
-
p
)
n
-
k
Doc 41
0.1590, 0.5657
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_process.html
p
1
p
2
(
1
-
p
3
)
Doc 58
0.1429, 0.2787
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Credit_default_swap.html
(
1
-
p
x
)
(
1
-
p
y
)
Doc 42
0.1558, 0.4365
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Odds_ratio.html
g
(
k
;
p
)
=
p
(
1
-
p
)
k
-
1
Doc 68
0.1347, 0.1347
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Yule–Simon_distribution.html
c
!
s
!
(
c
-
s
)
!
Doc 71
0.1325, 0.1325
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Proportional_approval_voting.html
n
!
m
!
(
n
-
m
)
!
Doc 69
0.1325, 0.1325
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Kummer's_theorem.html
Doc 70
0.1325, 0.1325
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Field_with_one_element.html
n
!
k
!
(
n
-
k
)
!
Doc 19
0.1789, 0.3115
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_theorem.html
Doc 28
0.1762, 0.3087
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Combination.html
Doc 49
0.1503, 0.5558
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
E
[
X
i
=
H
k out of n times
]
=
P
(
k
,
n
)
=
(
n
k
)
p
k
(
1
-
p
)
n
-
k
Doc 41
0.1590, 0.5657
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_process.html
∑
k
=
0
n
(
k
+
a
)
!
k
!
a
!
=
(
n
+
a
+
1
)
!
n
!
(
a
+
1
)
!
.
Doc 14
0.1870, 0.5747
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bose–Einstein_statistics.html
Doc 14
0.1870, 0.5747
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bose–Einstein_statistics.html
f
(
k
;
n
,
p
)
=
Pr
(
X
=
k
)
=
(
n
k
)
p
k
(
1
-
p
)
n
-
k
Doc 18
0.1789, 0.9645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_distribution.html
f
X
(
k
)
(
x
)
=
n
!
(
k
-
1
)
!
(
n
-
k
)
!
[
F
X
(
x
)
]
k
-
1
[
1
-
F
X
(
x
)
]
n
-
k
f
X
(
x
)
Doc 62
0.1402, 0.2686
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Order_statistic.html
p
(
1
-
p
)
n
f
(
x
p
)
2
Doc 72
0.1279, 0.1279
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Median.html
w
(
n
,
2
)
=
(
n
+
1
)
!
n
!
1
!
.
Doc 14
0.1870, 0.5747
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bose–Einstein_statistics.html
n
p
,
n
p
(
1
-
p
)
Doc 49
0.1503, 0.5558
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
X
-
n
p
n
p
(
1
-
p
)
Doc 18
0.1789, 0.9645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_distribution.html
Standard error
≈
p
(
1
-
p
)
n
Doc 73
0.1236, 0.1236
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Margin_of_error.html
s
p
=
p
(
1
-
p
)
n
Doc 74
0.1229, 0.2445
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Checking_whether_a_coin_is_fair.html
f
(
r
|
H
=
h
,
T
=
t
)
=
(
h
+
t
+
1
)
!
h
!
t
!
r
h
(
1
-
r
)
t
.
Doc 74
0.1229, 0.2445
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Checking_whether_a_coin_is_fair.html
g
n
(
p
)
=
n
p
(
1
-
p
)
Doc 18
0.1789, 0.9645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_distribution.html
F
S
T
=
var
(
𝐩
)
p
(
1
-
p
)
Doc 75
0.1215, 0.1215
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/F-statistics.html
𝒩
(
n
p
,
n
p
(
1
-
p
)
)
,
Doc 18
0.1789, 0.9645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_distribution.html
1
-
6
p
(
1
-
p
)
n
p
(
1
-
p
)
Doc 18
0.1789, 0.9645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_distribution.html
N
e
(
v
)
=
p
(
1
-
p
)
2
var
^
(
p
)
.
Doc 76
0.1122, 0.1122
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Effective_population_size.html
\Q
(
k
;
p
)
=
(
N
-
2
k
-
1
)
p
(
k
-
1
)
(
1
-
p
)
(
N
-
k
-
1
)
Doc 77
0.1092, 0.1092
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Incomplete_information_network_game.html
v
a
r
(
p
)
=
p
(
1
-
p
)
n
Doc 39
0.1619, 0.4277
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Binomial_proportion_confidence_interval.html
n
!
(
n
-
r
)
!
r
!
μ
r
(
1
-
μ
)
n
-
r
→
e
-
λ
λ
r
r
!
.
Doc 78
0.1066, 0.1066
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Return_period.html
p
d
i
(
1
-
p
)
n
i
b
-
d
i
2
-
(
N
-
n
i
)
b
Doc 79
0.1028, 0.1028
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Sequential_decoding.html
1
n
K
(
N
-
K
)
(
N
-
n
)
(
N
-
2
)
(
N
-
3
)
⋅
Doc 80
0.0921, 0.0921
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Hypergeometric_distribution.html
D
=
v
a
r
o
b
s
v
a
r
b
i
n
=
s
2
n
p
(
1
-
p
)
Doc 11
0.1916, 0.6465
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Taylor's_law.html