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5
Models for discrete random variables
5
Models for discrete random variables
Geometric type sums
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5.1
Useful mathematical identities
The following identities are helpful in the subsequent developments.
Arithmetic progression:
∑
i
=
1
n
i
=
n
(
n
+
1
)
/
2
.
Sum of squares:
∑
i
=
1
n
i
2
=
n
(
n
+
1
)
(
2
n
+
1
)
/
6
.
Exponential series:
exp
(
x
)
=
1
+
x
+
x
2
2
!
+
x
3
3
!
+
…
=
∑
i
=
0
∞
x
i
i
!
Note also that:
e
=
exp
(
1
)
exp
(
x
)
=
e
x
exp
(
x
+
y
)
=
exp
(
x
)
exp
(
y
)
exp
(
-
x
)
=
1
exp
(
x
)
Geometric type sums
Binomial expansion