Hint to the project exercise: ¡­

Hint to the project exercise: Threre seem to be many that are strugling with (b). In order to find the conditional distribution, find the bivariate (Gaussian) distribution for x(t) and y(t) conditional on x(t-1). This can be obtained by writting both x(t) and (y(t) as functions of x(t-1). Then from this bivariate distribution, find the conditional (Gaussian) distribution for x(t) given y(t). This gives the conditional distribution for x(t) given x(t-1) and y(t) (since we already have conditioned on x(t-1)). If still in trouble, take contact.