The joint probability distribution of two discrete random variables X and Y is given by the...

  

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The joint probability distribution of two discrete random variables X and Y is given by the following table: X 0 1 N 0 0 10 Y 1 0 i) What is the value of cov [X, Y]? ii) Are X and Y independent? Justify your answer. People in Galway withdraw money from a cash machine according to the fol lowing probability function (X): Amount (x) in € 50 100 200 P(X=x) The number of customers per day (N) has the distribution N Poisson(X). Let TN X₁ + X₂ + + Xy be the total amount of money withdrawn in a day, where each X, has the probability function above, and X₁, X₂.... are independent of each other and N. Therefore, Ty is a randomly stopped sum, stopped by the random number of N customers. i) Show that E(X)= 105 and Var(X)=2725. 0.30 0.5 0.2 ii) Find E(TN) and Var(Tv), i.e. the mean and variance of the amount of money withdrawn each day. The joint probability distribution of two discrete random variables X and Y is given by the following table: X 0 1 N 0 0 10 Y 1 0 i) What is the value of cov [X, Y]? ii) Are X and Y independent? Justify your answer. People in Galway withdraw money from a cash machine according to the fol lowing probability function (X): Amount (x) in € 50 100 200 P(X=x) The number of customers per day (N) has the distribution N Poisson(X). Let TN X₁ + X₂ + + Xy be the total amount of money withdrawn in a day, where each X, has the probability function above, and X₁, X₂.... are independent of each other and N. Therefore, Ty is a randomly stopped sum, stopped by the random number of N customers. i) Show that E(X)= 105 and Var(X)=2725. 0.30 0.5 0.2 ii) Find E(TN) and Var(Tv), i.e. the mean and variance of the amount of money withdrawn each day.

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