Question: Let our data be generated from a mixture of two univariate Gaussian distributions, where is a Gaussian with mean and , and is a Gaussian

Let our data be generated from a mixture of two univariate Gaussian distributions, where is a Gaussian with mean and , and is a Gaussian with mean and . The only unknown parameter is the mixing parameter (which specifies the prior probability of ). Now we observe a single sample . Which of the following equations is the correct likelihood function

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