Poisson sampling.

Let {X(t)} be a continuous-time Markov chain with stationary distribution \pi . We sample the chain at times given by an independent Poisson process: let N(t) be a Poisson process with rate \alpha , independent of the Markov chain, and define Yn= X(Tn +), the value taken by X immediately after the epoch Tnof the nth arrival of N. Show that {Yn} is a discrete-time Markov chain with the same stationary distribution as X.

3. A US company pays interest for $30,000 matured on its bonds held by a German investor. The payment is in Dollars. The German investor sells the Dollars to the European Central Bank (official institution). How do you record this transaction in the US Balance of Payments? Current Account $30,000 Financial Account (Non-official) (a) Financial Account (Official) $30.000 Current Account Financial Account (Non-official) (b) $30.000 $30,000 Financial Account (Official) Current Account $30.000 Financial Account (Non-official) (c) Financial Account (Official) $30,000 Current Account Financial Account (Non-official) (d) $30,000 Financial Account (Official) $30,000 3The capital and financial account for a fictitious country is shown in the table below. The balance on the current country is -$90 billion. a. Fill in the missing values in the table. Instructions: Enter your answers as whole numbers. Use a negative sign if necessary. CAPITAL AND FINANCIAL ACCOUNT (billions of dollars) (11) Balance on capital account Financial Account (12) Foreign purchases of domestic assets 204 (13) Domestic purchases of foreign assets (14) Balance on financial account 93 (15) Balance on capital and financial account b. The country has a capital and financial account (Click to select) (Click to select) surplus deficit\f