A dart is to be thrown at a target. The probability the dart will hit the target (yes or no) on a single attempt is 0.20. Each throw is independent of the other throws. Let X be the number of attempts before the target is hit. a. What type of distribution does X follow? State the name and parameters. b. Compute the expected number of attempts needed before hitting the target. c. What is the variance and standard deviation of the number of attempts needed before hitting the target? d. What is the probability that it will take less or equal to 4 throws before hitting the target? Write out the theoretical form and use R to compute a numeric value. e. Now say we want to hit the target twice. That is to say, we throw the dart until we hit the target once, and then keep throwing the dart until we hit the target a second time. What is the probability that it will take less than or equal to 4 throws to hit the target on both successful target hits? Write out the theoretical form and use R to compute a numeric value. f. Now say we want to hit the target twice. What is the expected number of total attempts needed to hit the target twice?