I have two random variables (x1 and x2) with known mean and variances. I need to calculate the expected value and confidence intervals for the sum of a and b trials respectively. Assume both are normally distributed and independent.
For example, x1 mean = 15, var = 5, x2 mean = 10 var =3
What is the confidence interval for sum(7 trials of x1, 6 trials of x2)? I can calc the expected value easily.
In words, I know that I sell on average 15 boxes of product x1 with variance 5 and 10 boxes of product x2 with variance 3 per day. I have 7 days of selling product x1 and 6 days of product x2 in the month. What is the confidence interval of my expected total sales for the remainder of the month?
I could brute force it with a monte carlo, but would prefer to just calc it...