Question

_{A random variable ? has a lognormal distribution with ? = 0 and ? = 1. Find ?(? < 1)}

Answer 1

Solution:

? has a log normal distribution with ? = 0 and ? = 1

Let Y = lox X   

(Note that this is log to the base e)

So , Y follows Normal distribution with ? = 0 and ? = 1

P(X < 1) = P(log X < log 1)

= P(Y < 0)

= P[(Y - )/ <  (0 - )/]

= P[Z <  (0 - 0)/1]

= P[Z < 0.00]

= 0.5 ..using z table.

P(X < 1) = 0.5