(3) (a) A fair coin is flipped, if it lands on the head side, one dice is rolled and X is the resulted number, if it lands on the tail side, two dice are rolled and X is the resulted sum. Calculate...

Extracted text: (3) (a) A fair coin is flipped, if it lands on the head side, one dice is rolled and X is the resulted number, if it lands on the tail side, two dice are rolled and X is the resulted sum. Calculate E[X] and V[X]. Write a computer program and carry out a simulation to verify your answers. (b*) A person starts walking home from a bar towards his home. The distance is n blocks. Every hour he either manages to walk one block towards home, or gets confused and picks up a cab back to the bar (each with probability 1/2). At any point, if he is at the bar, he always moves ahead one block. What is the expected time it takes him to get home? (c) Write a computer program' and carry out a simulation to verify your answer. (If you have trouble with part (b), do the computer simulation and formulate a conjecture of the answer for partial credits.)