Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Grinstead-Snell-Probability
· Problem 6.3.6
Sums of Random Variables
Mathematics · expected-value-variance-continuous
Problem
Let
T
T
T
be a random variable with range
[
0
,
∞
]
[0, \infty]
[
0
,
∞
]
and
f
T
f_T
f
T
its density function. Find
μ
(
T
)
\mu(T)
μ
(
T
)
and
σ
2
(
T
)
\sigma^2(T)
σ
2
(
T
)
if, for
t
<
0
t < 0
t
<
0
,
f
T
(
t
)
=
0
f_T(t) = 0
f
T
(
t
)
=
0
, and for
t
>
0
t > 0
t
>
0
, (a)
f
T
(
t
)
=
3
e
−
3
t
f_T(t) = 3e^{-3t}
f
T
(
t
)
=
3
e
−
3
t
. (b)
f
T
(
t
)
=
9
t
e
−
3
t
f_T(t) = 9te^{-3t}
f
T
(
t
)
=
9
t
e
−
3
t
. (c)
f
T
(
t
)
=
3
/
(
1
+
t
)
4
f_T(t) = 3/(1+t)^4
f
T
(
t
)
=
3/
(
1
+
t
)
4
.
Related theory
State Value And Action Value Functions
Browse the problem library