Drawing parallels to the $1 store example discussed in the lecture, answer the following questions: When Steph Curry shoots a free throw, he hits with a probability of 0.9 and misses with a probability of 0.1. Assume that the result of his previous free throw (whether a hit or a miss), does not affect the probability with which he hits the current throw, i.e., for any free throw he shoots, he hits with a probability of 0.9 and misses with a probability of 0.1. When he hits a free throw, he makes one point and when he misses a free throw, he makes zero points. Answer the following questions with this information Let P1 denote a random variable that represents the number of points Steph Curry makes when he shoots only one free throw. 1. How many possible values can P1 take? Develop a probability distribution for P1 (Very important: Enter the values of P1 in increasing order as you go down in the table) P1 f(P1) (1 decimal) (1 decimal) Let P2 denote a random variable that represents the number of points Steph Curry makes when he shoots two free throws. 2. How many possible values can P2 take? Develop a probability distribution for P2 (Very important: Enter the values of P2 in increasing order as you go down in the table) P2 F(P2) 12 decimal) 12 decimal) (2 decimal) Let PS denote a random variable that represents the number of points Steph Curry makes when he shoots five free throws 3. How many possible values can P5 take? 4. What is the probability that P5 is equal to 0? (5 decimals) 5. What is the probability that P5 is equal to 5? (5 decimals) Let P25 denote a random variable that represents the number of points Steph Curry makes when he shoots 25 free throws 6. How many possible values can P25 take? 7. E(P25)? (1 decimal) 8. Var(P25)? 12 decimals) 9. Stddev(P25)? (1 decimal) Let P100 denote a random variable that represents the number of points Steph Curry makes when he shoots 100 free throws 10. How many possible values can P100 take? 11. E{P100)? 12. Var(P100)? 13. Stddev(P100)? Let P1 denote a random variable that represents the number of points Steph Curry makes when he shoots only one free throw Consider the random variable 25 P1 14. Is E(P25) equal to E(25 P1)? Answer "Yes" or "No" 15. Is Var(P25) equal to Var(25 P137 Answer "Yes" or "No" 16. Is Stddev(p25) greater than Stedev(25 P1/7 Answer "Yes" or "No