A Gaussian mixture is a random variable whose PDF is a linear combination of two Gaussian PDFs,
![](https://test.transtutors.com/qimg/a8d72b5a-93a5-4d77-ad79-6b262ba12459.png)
(a) Find the moment-generating function, MX(u) , of the Gaussian mixture.
(b) Use the moment-generating function to find the mean of the Gaussian mixture.