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Mean of sum and difference of random variables

Mean of sum and difference of random variables.

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• Hi, can someone please clarify my basic confusion.Let's say if I have two hypothetical random independent variables X and Y like :

X : 1,2,3
Y : 4,5,6

Now if I have to combine these two variables what will be resultant output X+Y?
Will it be {1,2,3,4,5,6}
Or {5,7,9} ?
• You can't really add the random variables themselves but can add their means and std dev.
You would get mean:7
StdDev.:1.1547
• if you like maths so much name every number
• If we define a description of a number as a finite string of symbols that uses a finite alphabet of symbols, then there are only countably many descriptions. However, there are uncountably many real numbers. So almost all real numbers are indescribable!
• I still don't know whats a sum
(1 vote)
• the sum in a layperson's term would be the result when you add them together.
(1 vote)
• so is there a difference between an expected value and a mean? like can the mean be decimals like 5.6 but you can expect to see 5.6 cats, so would the expected value be 6 cause you would round this number upwards? or would it be 5 cause that would give you a more accurate expected value? or am i thinking too much and the expected value would actually just be equal to the mean and therefor be 5.6 ?
(1 vote)
• Expected value is the average value.

So, seeing 5.6 cats could very well be the expected value, even though it's definitely not the expected outcome of any given trial.
(1 vote)
• Does anyone know where I could find the proof video of this?
(1 vote)
• I'm also stuck here and how do we actually combine two random variables like literally how do we construct the resultant distribution?, what did you do?
(1 vote)
• Let's say I have the same dog and cat scenario scenario with the additional knowledge that we sampled our distributions in the same days and in the same ways, in that case lets say dogs = {3,4,5} and cats = {1,2,3}. can we say that animals = {3 + 1, 4 + 2, 5 + 3}?
(1 vote)
• The expected value is always a mean? A sample mean? A population mean?

Expected value is the sum of multiplying probabilities with their respective events? Weird.