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  3. let (x1, x2) have a bivariate normal distribution

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

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Basic Math

Let (X1, X2) have a bivariate normal distribution with meanvector (µ1, µ2), variance ? 12 for X1 and ? 22 for X2 and correlation cor(X1, X2) = ?.

(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 meanand variance of the conditional distribution.

(d) Obtain the likelihood equations and calculate the MLE forµ1, µ2, ?12 , ?2 2 , ?.

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