text: 9.x1 ~ n(0,3), x2 ~ n(0,3), and x3 ~ n(0,3). x1, x2 and x3 are all independent of each other. describe the dis 9.x1 ~ n(0,3), x2 ~ n(0,3), and x3 ~ n(0,3). x1, x2 and x3 are all independent of each other. describe the distribution of x1+ x2 + x3. what is p(x>0)?   (statistics questions) is 3 the standard deviation or the variance?  since x1, x2, and x3 are all nromal and independent, then   x1 + x2 + x3 ~ n(0+0+0 = 0, sqrt(3^2+3^2+3^2) = sqrt(27)), if 3 was the sd. n(0, 3+3+3 = 9) if 3 was the variance.  in general, if x_i ~ n(mu_i, sigma_i), where sigma_i is the sd, then the sum of x_i ~ n(sum mu_i, sqrt(sum (sigma_i)^2)).  since the mean of your distribution is 0, then p(x1+x2+x3>0) = 0.5.  remember that the mean splits the normal distribution in half.