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[Steps Shown] Sum of two normally distributed random variables Assume that X_1, X_2 are independent normally distributed random variables. Let the mean and

Question: Sum of two normally distributed random variables

Assume that \(X_{1}, X_{2}\) are independent normally distributed random variables. Let the mean and variance of \(X_{i}\) be equal to \(\left(\mu_{i}, \sigma_{i}^{2}\right)\). Compute the distribution of \(X_{1}+X_{2}\) by using the characteristic function.

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