Bill and Joe decided to go on vacation together. Bill lives in Boston, and Joe lives in New York. They flip a coin to decide if they will fly from Boston or from New York, and then they flip a coin again to decide if they will go to Miami or to Las Vegas. Flight time between Boston and New York is 1 hour, and flight times from either of these cities to Miami and Las Vegas are 3 hours and 5 hours respectively. Find the mathematical expectation, variance and standard deviation of the total flight time for Bill from his home city to their vacation destination.