I have three random variables ($A$, $B$, $C$). The mean of these variables are $12$, $5.6$, $0.2$ respectively. The standard deviations are $0.4$, $0.8$, $0.2$ respectively. The probability density function of each variable is normal (gaussian). The correlation coefficient is $0.5$ for each couples of variables. I would to calculate the mean of the random variable
$Z = e^{ABC}$
but I have no idea how to do that.
Furthermore, the exercise tell me to calculate the mean of $Z$ in the case $A$, $B$, $C$ are uniform (rectangular) with half-width $0.4$, $0.8$, $0.2$ respectively. This time, the correlation coefficient is $1$ for each couples of variables.
Unfortunately, my degree doesn't have a course in probability, so it could be a big help for me if you would explain me the intermediate steps.
Thank you in advance!