2. Assume that X ~ N(0,σ²). Show that E(eªx) = e²²², Va Є R. (1) Let S(t) = Soeμt+o√tz " (2) where Z ~ N(0, 1). Use (1) to find E[S(t)] and var(S(t).
2. Assume that X ~ N(0,σ²). Show that E(eªx) = e²²², Va Є R. (1) Let S(t) = Soeμt+o√tz " (2) where Z ~ N(0, 1). Use (1) to find E[S(t)] and var(S(t).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Assume that X ~ N(0, 02). Show that
E(eax) = e2:2, Va ER
Let
S(t) = Soekt+ovtz
where Z~ N(0, 1). Use (1) to find ElS(t)| and var (S(t)
![2.
Assume that X ~ N(0,σ²). Show that
E(eªx) = e²²²,
Va Є R.
(1)
Let
S(t)
=
Soeμt+o√tz
"
(2)
where Z
~
N(0, 1). Use (1) to find E[S(t)] and var(S(t).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F643c9073-bfc9-41d3-b50c-3b14187fea75%2Fc9310b00-3a07-45b4-980d-daae38ff2dbb%2F6a0ujn9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
Assume that X ~ N(0,σ²). Show that
E(eªx) = e²²²,
Va Є R.
(1)
Let
S(t)
=
Soeμt+o√tz
"
(2)
where Z
~
N(0, 1). Use (1) to find E[S(t)] and var(S(t).
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