Let (X1, X2) have a bivariate normal distribution with mean vector (µ1, µ2), variance σ 12...

Let (X1, X2) have a bivariate normal distribution with mean vector (µ1, µ2), variance σ 1² for X1 and σ 2 ² for X2 and correlation cor(X1, X2) = ρ.

(a) Write down the joint density f(x1, x2).

(b) Find the marginal distribution f(x1)

(c) Find the conditional distribution f(x1 | x2) and the mean and variance of the conditional distribution.

(d) Obtain the likelihood equations and calculate the MLE for µ1, µ2, σ1² , σ2 ² , ρ.

Expert Solution

milcah answered 1 year ago

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Question

Let (X1, X2) have a bivariate normal distribution with mean vector (µ1, µ2), variance σ 12...

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