## Normal Distributions

Hi say I have two "independent" Normal distributions,

S ~ N(0,3^2) and D~(0,2^2)

since I know that S and D are indpendent then

P(S ) + P(D) = P(S)P(D)

however we know they are both normal distributed so I amm just wondering what the general rule is for multiplying two normal distributions
thanks
 Recognitions: Homework Help I'm not sure what you mean by $$P(S) + P(D) = P(S) P(D)$$ Are you trying to say that when normal random variables are added, the resulting random variable is their product? Not true. If \begin{align*} S & \sim n(\mu_S, \sigma^2_S)\\ D & \sim n(\mu_D, \sigma^2_D) \end{align*} and they are independent, then the sum $$S + D$$ is normal, with mean $$\mu_S + \mu_D$$ and variance $$\sigma^2_S + \sigma^2_D$$ A similar result is true even if the two variables have non-zero correlation (the formula for the variance of the sum involves the correlation). If by 'product' $$P(S) P(D)$$ you mean the convolution of the distributions, you could go through that work, but it leads you to the same result I quoted above.

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 Quote by chota ... since I know that S and D are indpendent then P(S ) + P(D) = P(S)P(D)
I'm guessing you meant to say

P(S & D) = P(S)P(D)

where "S" here really means a statement along the lines of "S lies between A and B", and similarly for "D".

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 Recognitions: Homework Help I answered as I did because the OP used $$S, D$$ in his notation, and I took these as the names of the random variables rather than any interval or event. I took the question to mean he was asking how to combine normal distributions rather than calculate any particular probability