Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Grinstead-Snell-Probability
· Problem 10.1.8
Generating Functions
Mathematics · generating-functions-discrete
Problem
Let
X
1
,
X
2
,
…
,
X
n
X_1, X_2, \ldots, X_n
X
1
,
X
2
,
…
,
X
n
be an independent trials process, with values in
{
0
,
1
}
\{0, 1\}
{
0
,
1
}
and mean
μ
=
1
/
3
\mu = 1/3
μ
=
1/3
. Find the ordinary and moment generating functions for the distribution of (a)
S
1
=
X
1
S_1 = X_1
S
1
=
X
1
. Hint: First find
X
1
X_1
X
1
explicitly. (b)
S
2
=
X
1
+
X
2
S_2 = X_1 + X_2
S
2
=
X
1
+
X
2
. (c)
S
n
=
X
1
+
X
2
+
⋯
+
X
n
S_n = X_1 + X_2 + \cdots + X_n
S
n
=
X
1
+
X
2
+
⋯
+
X
n
.
Related theory
Characteristic Functions And Moment Generating Functions
Browse the problem library