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## Main Question or Discussion Point

Hi all,

I am having trouble finding information on a certain problem.

Consider you have a probability that $x_1 = x_a$ (in my case, the probability distribution is a normal distribution centred about 0). So:

$dp(x_1=x_a) = P(x_a) dx_a $

Also consider you have a second variable, $x_2$ for which you have:

$dp(x_2 = x_b) = P(x_b) dx_b$

So we know the probabilities of $x_1$ being $x_a$ and the probability of $x_2$ being $x_b$.

Now, what is the probability that $x_1 + x_2 = x_a + x_b = x_{tot}$?

My first thought was to double integrate dp(x_1=x_a)*dp(x_2 = x_b) with limits from -inf to +inf in both cases, but I think this will overestimate the probability.

I am having trouble finding information on a certain problem.

Consider you have a probability that $x_1 = x_a$ (in my case, the probability distribution is a normal distribution centred about 0). So:

$dp(x_1=x_a) = P(x_a) dx_a $

Also consider you have a second variable, $x_2$ for which you have:

$dp(x_2 = x_b) = P(x_b) dx_b$

So we know the probabilities of $x_1$ being $x_a$ and the probability of $x_2$ being $x_b$.

Now, what is the probability that $x_1 + x_2 = x_a + x_b = x_{tot}$?

My first thought was to double integrate dp(x_1=x_a)*dp(x_2 = x_b) with limits from -inf to +inf in both cases, but I think this will overestimate the probability.