Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% 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. 000 P=000 000 0 S=0 Proportion of games won by Doug = 0

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 6% chance of returning $11,000,000 profit, a 33% chance of returning $2,000,000 profit, and a 61% chance of losing the million dollars. The second company, a hardware company, has a 15% chance of returning $5,000,000 profit, a 29% chance of returning $2,000,000 profit, and a 56% chance of losing the million dollars. The third company, a biotech firm, has a 15% chance of returning $4,000,000 profit, a 26% of no profit or loss, and a 59% chance of losing the million dollars. Order the expected values from smallest to largest. first, second, third second, first, third second, third, first first, third, second third, first, second third, second, first Hint: Hint Video on Expected Value [+] Submit Question habits-9gegLPa 7- 17,164 5. 9. NOV 1. étv 16 3D MacBook Air

Chris and Ed decide to help each other by doing repairs on each other's houses. Chris is a carpenter and Ed is an electrician. Chris does carpentry work on his house as well as on Ed's house. Similarly, Ed does electrical repairs on his house and on Chris's house. When they are all finished they realize that Chris spent 42% of his time on his own house and 58% of his time on Ed's house, and that Ed spent 56% of his time on his own house and 44% of his time on Chris's house. If they originally agreed that the total of the work should amount to $9000, how much money should each get for their work?

Carl was competing on a game show, and he ran into a losing streak. First, he bet half of his money on one question and lost it. Then he lost one fourth of his remaining money on another question. Then he lost $300 on another question. Then he lost two-thirds of his remaining money on another question. Finally, he got a question right and won $200. At this point, the show ended, and he had $800 left. How much did he have before his losing streak began?

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 14% chance of returning $11,000,000 profit, a 37% chance of returning $2,000,000 profit, and a 49% chance of losing the million dollars. The second company, a hardware company, has a 8% chance of returning $6,000,000 profit, a 39% chance of returning $2,000,000 profit, and a 53% chance of losing the million dollars. The third company, a biotech firm, has a 5% chance of returning $9,000,000 profit, a 43% of no profit or loss, and a 52% chance of losing the million dollars. Order the expected values from smallest to largest. second, first, third second, third, first first, third, second first, second, third third, second, first third, first, second

USA. Benjamin Banneker (1731-1806) is one of the great American heroes of all time. The son and grandson of Africans captured and enslaved, he was fortunate to have been born free. He inherited the family farm where he worked hard all of his life. As a child he had a few months of schooling. Everything else he had to do on his own. He loved mathematics and science but did not get a chance to learn astronomy until he was in his fifties. Then he performed a near miracle, learning it all in less than a year. In his hand-written journal, he recorded two right triangle examples that interested him. You can solve them here and remember the great man who enjoyed geometry. On the page in his journal next to the August 1775 astronomy calculations, Banneker wrote, in the style of that time: Suppose a ladder 60 feet long be placed in a Street so as to reach a window on the one Side 37 feet high, and without moving it at bottom, will reach another window on the other side of teh Street which is 23…

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 11% chance of returning $5,000,000 profit, a 29% chance of returning $1,500,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 12% chance of returning $5,000,000 profit, a 28% chance of returning $3,500,000 profit, and a 60% chance of losing the million dollars. The third company, a biotech firm, has a 14% chance of returning $10,000,000 profit, a 33% of no profit or loss, and a 53% chance of losing the million dollars. Order the expected values from smallest to largest. third, first, second second, third, first first, second, third third, second, first second, first, third first, third, second

Complete the following probability distribution table: Probability Distribution Table P(X) 0.3 16 24 0.2 34 0.3 Submit Question

A student's course grade is based on one midterm that counts as 5% of his final grade, ono class project that counts as 10% of his final grade, a set of homework assignments that counts as 50% of his final grade, and a final exam that counts as 35% of his final grade. His midterm score is 66, his project score is 80, his homework score is 93, and his final exam score is 80. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above least 80 but less than 90 is a B, and so on. an A, a mean of at His overall final score is (Type an integer or a decimal. Do not round.)

A chef is trying out a new recipe he has been working on and wants to see if it will sell better than his old one. To find out, he performs an experiment where he randomly assigns 20 people to try his new recipe and 20 people to try his old one. He asks each group how much they would be willing to pay for their food, and he finds that the group with the old recipe would pay an average of $20.00 and the second would pay an average of $26.00. He then performs an independent samples t-test between these groups. a. Suppose the sample variance for the price of the chef’s old recipe is $2.00, and the sample variance for the new recipe is $3.00. Perform a one-tailed t-test at a significance level of α = 0.01 and explain what the result means (how does the new recipe compare to the old one?). b. To evaluate the magnitude of effect size, compute the estimated Cohen’s d. Briefly describe what it means, and comment on the strength of the effect: is it weak, moderate or strong?