I have reached a stage where I need to solve for an unknown number, $\theta$ . However, I stuck and don't know how to proceed further.
The equation to be solved is:
$E\left[ \exp(\theta a^i) * a^i\right] = E\left[ \exp(\theta a^i)\right]* C$
where it is assumed that $a^i$ is a RV with the following assumption $\log(a^i) \sim N (\mu, \sigma^2)$. That is the logarithm of $a^i$ is normally distributed. Also, C is a parameter with known value.
Does anybody here help me on how to proceed to solve for the unknown $\theta$ ?