Lognormal distribution L1.T2.119
AIM: L1.T2.119. Describe the key properties of the lognormal distribution
Questions:
119.1 If the variable (Y) is a normal random variable, such than Y ~ N(mu, sigma^2), which of the following (X) variables is lognormally (log-normally) distributed?
- a. X = EXP(Y) = e^Y
- b. X = LN(Y)
- c. X = Y(1) + Y(2) + ... Y(n)
- d. X = LN[Y(2)/Y(1)]
119.2 Assume today’s stock price S(0) is $100, the daily log (continuously compounded) return has mean of 0.0 and standard deviation of 0.10 (10%), and tomorrow’s stock price is lognormally distributed. What is the approximate probability that tomorrow’s stock price will exceed $117.94?
- a. about 1%
- b. 1.43%
- c. 4.46%
- d. about 5%
119.3 Each of the following is TRUE about the lognormal distribution EXCEPT
- a. Is always non-negative with positive skew and leptokurtic (heavy tailed)
- b. If price S(t) is lognormal, then LN[S(t)] is normal
- c. The sum of lognormal variables is also lognormal
- d. The product of lognormal random variables is also lognormal
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