Question 12 (2 points) Assume that X and Yare Discrete Random Variables with the Probability Distributions given below: 1 x 2 3 1 0.11 0.46 0.04 у 2 0.01 0.01 0.16 3 0.07 0.01 0.13 What is the probability that x takes a value of 1 while y takes on a value of 2? Express your answer rounded to two decimal points. Hint: this is called the joint probability of x=1 and x=2. A

Question A local real estate investor in Kingston is considering three investments: a motel, a restaurant, or a theatre. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourist; Profits from the theatre will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment:   Real Estate Investor Payoff Table   Payoffs are Profits   States of Nature (Gasoline Avaliability) Decision Alternatives Shortage Stable Supply Surplus Motel $8,000 $15,000 $22,000 Restaurant $2,000 $8000 $6,000 Theater $6,000 $6,000 $5,000     Which option should the real estate investor choose if he uses the Equal Likelihood criterion? Using a maximax approach, what alternative should the real estate investor choose? Using the Maximum approach, what alternative should the real estate investor choose?

Question A local real estate investor in Kingston is considering three investments: a motel, a restaurant, or a theatre. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourist; Profits from the theatre will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment:   Real Estate Investor Payoff Table   Payoffs are Profits   States of Nature (Gasoline Avaliability) Decision Alternatives Shortage Stable Supply Surplus Motel $8,000 $15,000 $22,000 Restaurant $2,000 $8000 $6,000 Theater $6,000 $6,000 $5,000     If the probability of a shortage of gasoline is 25%, the probability of a stable supply of gasoline is 45% and the probability of a surplus of gasoline is 30%. Using the EMV, What option should the real estate investor choose and what is that optimal expected value? What is the most the real…

QUESTION 34 Suppose the actual sales and the forecasted, or smoothed sales, for the past 5 months have been Actual Smoothed 54.4   76.8 54.4 75.5 72.3 53.2 74.8 39.2 57.6 What is the Mean Absolute Error of the smoothed series? (please round your answer to 1 decimal place)