I have one variable, $X$, which is provided hourly for a period of one month (720 total values in the series). I have another variable, $Y$, which is provided quarterly (for which I am provided the average value and standard deviation, but not sure how many values in the population).
I am trying to find out the probability that the product of these values ($Z=XY$) will not exceed some limit, $L$.
Question: How can I calculate the standard deviation (thus the probability of exceeding $L$) of this product, $Z$, if the number of measurements is not equal in $X$ and $Y$?