Which distribution do the following random variables follow? State their parameters explicitly, (e.g, if the random variable follows the binomial distribution, state both the values of n and p.) If the random variable does not follow any "named" distribution from class, briefly describe how you might construct a probability mass function for it.

(a) A thumbtack will land with the point directly up 30% of the time. It is repeatedly flipped until it lands point up twice. Let U be the number of times to thumbtack is flipped.

(b) A specific textbook has a 10% chance of falling apart after a semester of use. If a class of 30 all has this textbook, let V be the number of textbooks that have fallen apart by the end of the semester.

(c) An archer hits her target with probability 0.6. Let W be the number of arrows she shoots in order to hit the target 5 times.

(d) A machine that makes pencils makes correctly made pencils with probability 0.99. The boss asks to see what a defective pencil looks like, and waits until a defective pencil is made. Let X be the number of pencils that the boss watches made.

(e) (continued from (d)...) If 10 pencils come in a box, let Y be the number of correctly made pencils in a given box.

(f) I have 10 pencils in my drawer, but only two are sharpened. I randomly choose pencils from my drawer one at a time until I find a sharp one. I don't bother to return the unsharpened pencils to my drawer before choosing again. Let Z be the number of pencils I choose from my drawer.