- #1
natski
- 267
- 2
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.