In each problem, make sure that you are clearly defining random variables, stating their distributions, and writing down the formulas that you are using. (That is, write down the pmf, write down mean and variance formulas.
6. John has been talking some mad smack about Fred, claiming to be leagues better than Fred at rock-paper-scissors. Suppose that despite talking some smack, John is just plain whack, and Fred is the better player, with a probability of 0.6 of winning any game against John. Fred challenges John to a match to defend his honor.
a. Suppose the match format is best of 5 - the first player to win three games is declared the winner. Assume matches are independent of one another. What is the probability that Fred wins the game in
In each problem, make sure that you are clearly defining random variables, stating their distribu...
In each problem, make sure that you are clearly defining random variables, stating their distributions, and writing down the formulas that you are using. (That is, write down the pmf, write down mean and variance formulas.) 1. Suppose we have a computer program that attempts to answer a yes or no question for us. The probability that the program will return the correct response 0.6. Suppose we run the program 15 times. Let X be the total number of times...
In each problem, make sure that you are clearly defining random variables, stating their distributions, and writing down the formulas that you are using. (That is, write down the pmf, write down mean and variance formulas.) Prove that the exponential distribution is memoryless. That is, let X~Exp(?), and show that for any two positive real numbers x, y, P(X ≥ x + y | X ≥ y) = P(X ≥ x). Hint: Mirror the proof we did in class for...