fluidistic
Gold Member
- 3,928
- 272
Homework Statement
Let X be a continuous random variable with parameters \langle x \rangle and \sigma.
Calculate the probability density of the variable Y=exp(X). Calculate the mean and the variance of Y.
Homework Equations
Reichl's 2nd edition book page 180:
P_Y(y)=\sum _{-\infty}^{\infty} \delta (y-H(x))P_X(x)dx where H(x)=Y, so I guess, H(x)=exp (x).
The Attempt at a Solution
I used the given formula and reached P_Y(y)=P_X (\ln y). Is this the correct answer?
I don't really know how to calculate the mean, \langle y \rangle. I guess they want it in function of the mean of X, namely \langle x \rangle.
I know that \langle x \rangle=\int _{-\infty}^{\infty} xP_X(x)dx and that \langle y \rangle=\int _{0}^{\infty} yP_Y(y)dy. But this does not help me much. Any idea on how to continue further?