Formulario di statistica
Calcolo combinatorio
𝐷!,# = 𝑛 ∗
(
𝑛−1
)
∗ …∗ (𝑛 − 𝑘 +1)
𝐷!,#
∗= 𝑛#
𝐶!,# =
-
𝑛
𝑘
.
=𝑛!
𝑘! ∗
(
𝑛−𝑘
)
!
Probabilità
𝑃
(
𝐴∪𝐵
)
= 𝑃
(
𝐴
)
+𝑃
(
𝐵
)
−𝑃(𝐴∩ 𝐵)
𝑃(𝐴/𝐵) = 𝑃(𝐴 ∩ 𝐵)
𝑃(𝐵)
𝑇𝑒𝑜𝑟𝑒𝑚𝑎<𝑑𝑖<𝐵𝑎𝑦𝑒𝑠:<𝑃
(
𝐴/𝐵
)
=𝑃
(
𝐵/𝐴
)
∗𝑃(𝐴)
𝑃(𝐵)
𝑇𝑒𝑜𝑟𝑒𝑚𝑎<𝑑𝑒𝑙𝑙𝑒<𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡à<𝑡𝑜𝑡𝑎𝑙𝑖: 𝑃
(
𝐴
)
=
G
𝑃
(
𝐴/𝐵%
)
∗𝑃
(
𝐵%
)
<𝑐𝑜𝑛<𝐵%=𝑝𝑎𝑟𝑡𝑖𝑧𝑖𝑜𝑛𝑒<𝑑𝑖<𝐴
#
%&'
Media:
𝐸
(
𝑋
)
=<
∑
𝑥%𝑝%%
Varianza:
𝑉𝑎𝑟
(
𝑋
)
= 𝐸
[
𝑋 − 𝐸
(
𝑋
)]
(= 𝐸
[
𝑋(
]
−𝐸([𝑋]
Distribuzioni di probabilità
𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑧𝑖𝑜𝑛𝑒<𝑏𝑖𝑛𝑜𝑚𝑖𝑎𝑙𝑒<𝑥~𝐵𝑖
(
𝑛,𝑝
)
:𝑃
(
𝑥 = 𝑘
)
=
-
𝑛
𝑘
.
∗𝑝#∗
(
1− 𝑝
)
!)#
(Media: n*p; Varianza: n*p*(1-p) )
𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑧𝑖𝑜𝑛𝑒<𝑛𝑜𝑟𝑚𝑎𝑙𝑒<𝑥~𝑁
(
𝜇,𝜎(
)
<𝑓𝑢𝑛𝑧𝑖𝑜𝑛𝑒<𝑑𝑖<𝑑𝑒𝑛𝑠𝑖𝑡à:< '
*
√
(, 𝑒)
(
.)/
)
!/(*!
𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑧𝑎𝑧𝑖𝑜𝑛𝑒:𝑃
(
𝑋 < 𝑥
)
= 𝑃
-
𝑍 < 𝑥 − 𝜇
𝜎
.
= Φ(<𝑥 − 𝜇
𝜎)
𝐴𝑝𝑝𝑟𝑜𝑠𝑠𝑖𝑚𝑎𝑧𝑖𝑜𝑛𝑒<𝑑𝑖<𝑢𝑛𝑎<𝑏𝑖𝑛𝑜𝑚𝑖𝑎𝑙𝑒<𝑐𝑜𝑛<𝑢𝑛𝑎<𝑛𝑜𝑟𝑚𝑎𝑙𝑒<
(
𝑛<𝑔𝑟𝑎𝑛𝑑𝑒<𝑒<𝑝<𝑝𝑖𝑐𝑐𝑜𝑙𝑎
)
:<
<𝜇 = 𝑛 ∗ 𝑝;<𝜎 =
]
𝑛∗𝑝(1− 𝑝)
