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5. [Joint Distribution] Determine the joint distribution of the two random variables, X and Y, whose distributions are below, given that the random variables are independent: Value of X: 0 1 Probability: 0.2 0.8 Value of Y: -1 1 Probability: 0.5 0.5 2 6. In a certain course, the homework average is worth 10% of the grade, the quiz average is worth 15% of the grade, and the three exams are each worth 25% of the grade. What is the course grade of someone with the following scores? How does this relate to probability? Homework 95 Average Quiz Average 80 Exam 1 75 Exam 2 89 Exam 3 92 7. A jar contains 21 pennies (worth $0.01 each), 15 nickels (worth $0.05 each), 18 dimes (worth $0.10 each), and 32 quarters (worth $0.25). If a coin is drawn at random, what is the expected value of the draw? 8. nt Toss a coin until it lands heads, then stop. The number of tosses is a random variable. What is the expected value of this random variable? (a) Guess what the expected number of tosses should be, and explain. (b) Set up the infinite series that equals the expected value, and show that it converges to something greater than 1