Problem 18.34. Which random variables (measurements) are Binomial? The number of successes is Binomial if: (i) The experiment counts successes in a fixed number of binary (succeed/fail) trials. (ii) Each trial has a fixed probability p of success. (iii) The trials are independent of each other. (a) Randomly answer 20 multiple-choice questions (5 choices each). Count the number correct. (b) Flip a biased coin (probability p of H) and count the number of heads in 100 flips. (c) Flip a biased coin until 2 heads appear (probability p of H) and count the number of flips. (d) A college admissions officer randomly samples students from 1,000 applications until they find four from NY-state. Count the number of applications sampled. (e) A college admissions officer randomly samples 100 students without replacement from 1,000 applications and counts the number of applicants from NY-state. (f) A college admissions officer randomly samples 100 students with replacement from 1,000 applications and counts the number of applicants from NY-state. (g) A Gallup poll randomly samples 1,000 Americans (without replacement) and asks them if they own an SUV. We count the number of SUV-owners among those polled. (h) The number of darts you throw until you hit the bulls-eye. (i) The number of darts hitting the bulls-eye if you throw 3 darts. (j) Hats of 100 men are given back to the men randomly. Count how many men get their hat back. (k) Each vertex of a graph is randomly placed into one of two sets A or B. The graph has m edges. A cut-edge has its vertices in different sets. We count the number of cut edges. (1) Draw 10 cards from a shuffled deck and count the number of aces. (m) You have 10 shuffled decks. Draw one card from each deck and count the number of aces. (n) Let X be the number of Is in the BITWISE-OR of two 10-bit sequences of independent random bits (1/0 are T/F). For example,0001110010 BITWISE-OR 1000111000 = 1001111010). (o) Toss 20 fair coins and re-toss (just once) all coins which flipped H. Count the number of: (i) Coins showing heads at the end. (ii) Heads tossed in the experiment. (p) Your total winnings in 100 fair coin flips when you win $2 per H and lose $1 per T. (q) A box has 50 bulbs in a random order, with 5 being defective. Of the first 5 bulbs, count the number defective