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9. Roll two fair dice and observe two numbers X and Y. (a) Find the probability that both numbers are greater than 3. (b) -" Find the probability that at least one number is greater than 3. (c) (Find the probability that X is greater than 3 given that Y' is less than 3. (d) ( Find the probability that the sum of the two numbers is 7. 10. Suppose your company makes sports bikes. 90% of the bikes are good and the rest are defective. Now you make 4 inspections at random. What is the probability that exactly 3 of them are good to go?11. Suppose that you are looking for a student at your college who lives within five miles of you. You know that 60% of the 25,000 students do live within five miles of you. You randomly contact students from the college until one says he or she lives within five miles of you. What is the probability that you need to contact exactly four people (including the one who gives positive answer)? 12. Suppose X is a continuous random variable with PDF given by fx(x) = 1 -e ( ) Define a new random variable Z = X - H Find the PDF of Z