If ln(x) has a normal distribution N(0,1) how do I find and prove the distribution for x?
And if S(t)=S(0)exp((mu-(sigma^2)/2)t+sigma*sqrt(tao)*G), where G N(0,1) what is the density function for S(t)?
If ln(x) has a normal distribution N(0,1) how do I find and prove the distribution for x?
And if S(t)=S(0)exp((mu-(sigma^2)/2)t+sigma*sqrt(tao)*G), where G N(0,1) what is the density function for S(t)?
Hello,
Click on the "picture" to see the code
Anyway, there's a latex sub-forum, where you may be able to learn some things about writing equations.
But what is "tao" ?
The pdf of isIf ln(x) has a normal distribution N(0,1) how do I find and prove the distribution for x?
Now, I can never remember the method you guys use... But mine is similar, using the Jacobian of the transformation.
For any bounded and continuous function f, we have :
Make the substitution :
So
Thus the pdf of is , for x>0
Which is the pdf of the log-normal distribution, with parameters (0,1).