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Bicen Maths
Statistics
Binomial Distribution
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Binomial distribution:
X
∼
B
(
n
,
p
)
X\ \sim B\left(n,p\right)
X
∼
B
(
n
,
p
)
How to calculate
P
(
X
<
a
)
P\left(X\ <\ a\right)
P
(
X
<
a
)
?
P
(
X
≤
a
−
1
)
P\left(X\ \le a-1\right)
P
(
X
≤
a
−
1
)
How to calculate
P
(
a
<
X
≤
b
)
P\left(a\ <\ X\ \le b\right)
P
(
a
<
X
≤
b
)
?
P
(
X
≤
b
)
−
P
(
X
≤
a
)
P\left(X\ \le b\right)\ -\ P\left(X\ \le a\right)
P
(
X
≤
b
)
−
P
(
X
≤
a
)
What should we do for inverse probabilities?
use the provided
tables
!
P
(
X
=
r
)
P (X = r)
P
(
X
=
r
)
=
(
r
n
)
p
r
(
1
−
p
)
n
−
r
(^n_r)p^r(1 - p)^{n-r}
(
r
n
)
p
r
(
1
−
p
)
n
−
r
