Bob and doug play a lot of ping-pong, but doug is a much better player, and wins 80% of their games. to make up for this, if doug wins a game he will spot bob five points in their next game. if doug wins again he will spot bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as long as he keeps winning. whenever bob wins a game he goes back to playing the next game with no advantage. it turns out that with a five-point advantage bob wins 20% of the time; he wins 40% of the time with a ten-point advantage and 70% of the time with a fifteen-point advantage. model this situation as a markov chain using the number of consecutive games won by doug as the states. there should be four states representing zero, one, two, and three or more consecutive games won by doug. find the transition matrix of this system, the steady-state vector for the system, and determine the proportion of games that doug will win in the long run under these conditions.

Listed below are time intervals (min) between eruptions of a geyser. assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. does it appear that the mean time interval has changed? is the conclusion affected by whether the significance level is 0.10 or 0.01? recent 78 90 90 79 57 101 62 87 71 87 81 84 57 80 74 103 62 past 88 89 93 94 65 85 85 92 87 91 89 91 follow the steps of hypothesis testing, including identifying the alternative and null hypothesis, calculating the test statistic, finding the p-value, and making a conclusions about the null hypothesis and a final conclusion that addresses the original claim. use a significance level of 0.10. is the conclusion affected by whether the significance level is 0.10 or 0.01? answer choices below: a) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10. b) no, the conclusion is not affected by the significance level because h0 is not rejected regardless of whether a significance level of 0.10 or 0.01 is used. c) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01. d) no, the conclusion is not affected by the significance level because h0 is rejected regardless of whether a significance level of 0.10 or 0.01 is used.