## quiz- probability and distribution

sandipkumarshaw
Good Student
Posts: 25
Joined: Thu Jan 30, 2014 3:37 pm

### quiz- probability and distribution

For a lognormal variable X, we know that ln(X) has a normal distribution with a mean of zero and a standard deviation of 0.5. What are the expected value and and the variance of X?
a. 1.025 and 0.187 Incorrect
b. 1.126 and 0.217 Incorrect
c. 1.133 and 0.365 Correct
d. 1.203 and 0.399 Incorrect
We have E[X] = exp[mu+0.5*sigma2] = exp[0+0.5 * 0.52] =1.1331. Assuming there is no error in the answers listed for the variance, it is sufficient to find the correct answer for the expected value.
My question is from where sigma2 value (0.52) has arrived?

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### quiz- probability and distribution

E[X] = exp[mu+0.5*sigma2] = exp[0+0.5 * 0.52(This is .5^2)] =1.1331.

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### quiz- probability and distribution

Usually the asset returns are normal . But when they are skewed to one direction they are lognormal distribution.For eg a \$100 stock can go upto \$300 but cannot go down to -\$150 . The lognormal distribution is skewed to the right .