Probability and Statistics

Can you please answer the questions and show your work. Thank you

• A game played with a fair eight-sided die, as pictured below. The player rolls the die. The player loses $6 if a 1,2,3, or 4 is rolled. On a roll of 5, 6, 7, 8 the player wins that amount.

Suppose the game is played 20 times. Let Y be the random variable that counts the number of times that an 8 is rolled. What is the probability P(Y=5) ? * Again, let Y be the random variable that counts the number of times that an 8 is rolled when the game is played 20 times. If we approximate the random variable Y by the Poisson random variable with parameter A, then we should choose the parameter A to be * Suppose the game is played until an 8 is rolled. Let 2 be the random variable that models the number of rolls required to get an 8. What kind of random variable best models 2? * O Geometric with p=1/8 Binomial with p=1/8 Poisson with A = 7/8 Negative Binomial with p='l/8 OOOO Hypergeometric with n=8 Suppose the game is played until an 8 is rolled. What kind of random variable models this event? Let 2 be the random variable that models the number of rolls required to get an 8. What is P(Z a 4)? * 0 159/512 0 343/512 \f