Howtosignalprocessing
- Is the sum of two dependent normal distributions normal?
- Can you combine normal distributions?
- Is the sum of 2 Gaussians Gaussian?
- How do you sum random variables?
Is the sum of two dependent normal distributions normal?
If they are dependent you need more information to determine the distribution of the sum. If and are iid and and are independent then X and Y are normally distributed (and then so are and ). If and form a bivariate normal distribution, then their sum is normal.
Can you combine normal distributions?
When we combine variables that each follow a normal distribution, the resulting distribution is also normally distributed. This lets us answer interesting questions about the resulting distribution.
Is the sum of 2 Gaussians Gaussian?
If X and Y are jointly Gaussian, then aX+bY (a and b are both constant) is also Gaussian. If X and Y are Gaussian and uncorrelated (hence independent), then aX+bY (a and b are both constant) is also Gaussian.
How do you sum random variables?
Let X and Y be two random variables, and let the random variable Z be their sum, so that Z=X+Y. Then, FZ(z), the CDF of the variable Z, would give the probabilities associated with that random variable. But by the definition of a CDF, FZ(z)=P(Z≤z), and we know that z=x+y.
