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What happens when you subtract two normal distributions?
In other words, the mean of the combined distribution is found by SUBTRACTING the two individual means from each other. Even though we are subtracting the distributions, variability is still increasing, so we still add the variances together.
Is the difference of two normal distributions normal?
If and are independent, then will follow a normal distribution with mean μ x − μ y , variance σ x 2 + σ y 2 , and standard deviation σ x 2 + σ y 2 . The idea is that, if the two random variables are normal, then their difference will also be normal.
How to add and subtract normal distributions in statistics?
More generally, if X 1, …, X n are independent normal random variables with means μ i and variances σ i 2, and c 1, …, c n are constants, Y = c 1 X 1 + … + c n X n is normal with mean μ Y = c 1 μ 1 + … + c n μ n and variance c 1 2 σ 1 2 + … + c n 2 σ n 2. Here you’re doing the case n = 3 with c 1 = − 1, c 2 = 1, c 3 = 1. You did this right.
Which is a normal distribution of B + C − a?
You did this right. The short way to look at it is that B + C − A is normally distributed with mean being μ = μ B + μ C − μ A and σ 2 = σ B 2 + σ C 2 + σ A 2. The key point you need to know is that a variate made of the sum of two independent normal variates is itself normally distributed, even if the means of those two variates are not the same.
Where can I find the normal difference distribution?
Weisstein, Eric W. “Normal Difference Distribution.” From MathWorld –A Wolfram Web Resource. https://mathworld.wolfram.com/NormalDifferenceDistribution.html The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine.
Is the sum of two random variables a normal distribution?
If you have two random variables that can be described by normal distributions and you were to define a new random variable as their sum, the distribution of that new random variable will still be a normal distribution and its mean will be the sum of the means of those other random variables.