Variance

It's the same E. That's just how variance is defined. You can apply the expected value operator, E, to other things besides besides just a single variable. More on reddit.com

Typically, when trying to prove things, it's helpful to state what you're trying to prove. For example, I don't know how to help you because you haven't written what statement, theorem, fact, formula, identity, etc, ... that you're trying to prove. Also, you need to define your symbols, which, without context, are meaningless. More on reddit.com

I have to ask though, what is "/(1-n)" That should be (N-1), according to Wikipedia , assuming that p = K/N. More on reddit.com

I'm embarrassed to present such a simple solution. The solution by u/CartesianJoin seems complete and was quick to come up with while I was preparing this one. Since I don't usually throw away work, here it goes. It was based on two theoretical items and an observation of practice. The most common is that prices in a non-controlled competitive market have a normal distribution, the majority of suppliers within an average range, and two minorities of similar sizes: the first below the average minus the standard deviation (Low price) and the second above the average plus the standard deviation (High price). When companies conduct price surveys among suppliers, they consult prices for at least five, depending on the product or service between 3 and 7 suppliers. They rarely use statistical data on market prices because there are contextual price fluctuations that statistics cannot track. Frequently updated, the Supplier/Cost Database is a small sample, often not representative, to obtain a snapshot of the market in terms of mean and standard deviation, thus hiding discrepancies. To compensate for the sample size, a common method among economists is used when there is no updated data, or the data is unknown, of market prices for specific products and services, the sample mean with a fixed standard deviation of 10% of the mean. The range of price variation between suppliers is 'normally' narrow because production is much more concentrated than distribution. Unit Cost (Col. C): random values ​​​​created by NORMINV, mean = 1, stdev = 1. Five suppliers (A through E), 8 products (#1 through #8), where not all suppliers supply all 8 products. The average market price of each item is based on the number (#n) of items, Item #1 has a $100 average price, Item #2 has a $200 average price, Item #3 has a $300 average price, and so on. StDev/Item (Col. E, standard deviation per Item): 10% of the average price, so Item #1 has a $10 standard deviation, Item #2 has a $20 standard deviation, Item #3 has a $30 standard deviation, and so on. If the average market price is unknown, this column can be calculated as: = 10% * [Ave./Item] (see below) Ave./Item (Col. D): Formula in INT format (semicolon separator) = ROUND( AVERAGE( IF(B2 = B$2:B$36; C$2:C$36; "") ); 0 ) Formula in US format (comma separator) = ROUND( AVERAGE( IF(B2 = B$2:B$36, C$2:C$36, "") ), 0 ) Price distribution (Col. F): Formula in INT format (semicolon separator) = IFS(C2<=D2-2*E2; "Very Low price"; C2<=D2-E2; "Low price"; AND(C2>D2-E2; C2=D2+E2; C2=D2+2*E2; "Very high price") Formula in US format (comma separator) = IFS(C2<=D2-2*E2, "Very Low price", C2<=D2-E2, "Low price", AND(C2>D2-E2, C2=D2+E2, C2=D2+2*E2, "Very High price") I hope this helps. More on reddit.com