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
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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).
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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