Part 1: Prove that the expectation and the variance of a lognormal random variable X with mean µ, standard deviation o and a normal random variable W with mean 0, standard deviation o has the following relation: (Note: You must prove the relation from both sides!) E(X)= µ=e®+*2 +1 Var (X)=o = e*+* (e -1) 0 = In u-

MATLAB: An Introduction with Applications
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Part 1:
Prove that the expectation and the variance of a lognormal random variable X with mean u,
standard deviation o and a normal random variable W with mean 0, standard deviation
o has the following relation:
(Note: You must prove the relation from both sides!)
E(X)= µ=e®+*2
O = Jln
+1
Var (X)=o = e0+* (e -1)
0 = In u-
Transcribed Image Text:Part 1: Prove that the expectation and the variance of a lognormal random variable X with mean u, standard deviation o and a normal random variable W with mean 0, standard deviation o has the following relation: (Note: You must prove the relation from both sides!) E(X)= µ=e®+*2 O = Jln +1 Var (X)=o = e0+* (e -1) 0 = In u-
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