The normal distribution of MLE is start {x1,,,,,xn} random sample from N(u,σ^2)

This family of distributions has two parameters: θ = (μ, σ), so we maximize the likelihood, , over both parameters simultaneously using logarithm...

I know this. but what if the normal distribution's {x1,,,,,xn} random sample from N(u,σi^2)

I mean the variance is not homoscedasticity. now the variance is heteroskedasticity...

I atteched the image. My questions is that What is the MLE if variance change σ^2 to σi^2.

σ^2 - homoscedasticity,

σi^2- variance is heteroskedasticity.

So

f(x/u, σi^2) = 1/sqrt(2pi)σi exp((x-u)^2/2σi^2

I don't know.... How can I solved...

This family of distributions has two parameters: θ = (μ, σ), so we maximize the likelihood, , over both parameters simultaneously using logarithm...

I know this. but what if the normal distribution's {x1,,,,,xn} random sample from N(u,σi^2)

I mean the variance is not homoscedasticity. now the variance is heteroskedasticity...

I atteched the image. My questions is that What is the MLE if variance change σ^2 to σi^2.

σ^2 - homoscedasticity,

σi^2- variance is heteroskedasticity.

So

f(x/u, σi^2) = 1/sqrt(2pi)σi exp((x-u)^2/2σi^2

I don't know.... How can I solved...

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