Dene discrete random variables as follows: 0 X = number of rolls ofa 4-sided, fair die (i.e. faces labeled 1-4) until a 2 turns up. 0 Y = number of ips of a fair 2-sided coin that turn up heads out of 5 total ips. 0 Z = number shown on a card drawn randomly from a III-card deck with cards labeled 1-10. 1. Classify the distribution for each random variable (i_e. discrete uniform, binomial, negative binomial, geometric, hypergeometric, Poisson, or multinomial.) 2. Calculate the mean and variance for all three random variables (X, Y, and Z). 3. Calculate the probability that Y is equal to 3. |:' 4. Calculate the probability that X is 2 or more. |:| 5. Calculate the probability that Z is a prime number (i.e. equal to 2, 3, 5, or 7). |:| 6. Define an experiment as repeatedly drawing cards, with replacement, from the lD-card deck, checking if each card drawn is a prime number (i.e. the card is drawn, the number recorded as either prime or not, the card is placed back in the deck, and then shufed before the next draw). This process is used to draw 8 cards total and count how many of the 8 cards are prime. a. ls this a Bernoulli process? Justify your answer, addressing all required aspects of a Bernoulli process. b. Calculate the probability that at least 3 of the cards drawn are prime. |:|