Two players receives a ticket t each on which there is a number in [0, 1]. The number on a player's ticket is the size of a prize that he may receive. The two prizes are identically and independently distributed according to a uniform distribution. Each player is asked independently and simultaneously whether he wants to exchange his prize for the other player's prize. If both players agree then the prizes are exchanged; otherwise each player receives his own prize. Find the Bayesian Nash equilibrium of this game.
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- A graduate student conducted an experiment in which 15 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two occasions, the baby witnesses the character fail to make the climb. On the third attempt, the baby witnesses either a helper toy push the character up the hill or a hinderer toy prevent the character from making the ascent. The helper and hinderer toys were shown to each baby in a random fashion for a fixed amount of time. The baby was then placed in front of each toy and allowed to choose which toy he or she wished to play with. In 13 of the 15 cases, the baby chose the helper toy. Complete parts (a) through (d) below. (a) Why is it important to randomly expose the baby to the helper or hinderer toy first? A. The randomness in the order of exposure is important to make sure half the babies see the helper first and the other half see the hinderer first. B. The randomness in the order of exposure is important to…An experiment was performed with three treatments (A, B, and C). Which of the following is a correct model with a categorical explanatory variable with three categories? yˆ = a +bx where x = 0 if in treatment A, x = 1 if in treatment B, and x= 2 if in treatment C yˆ = a +bxA + cxB + dxC where xA = 1 if in treatment A, and = 0 if not in treatment A xB = 1 if in treatment B, and = 0 if not in treatment B xC = 1 if in treatment C, and = 0 if not in treatment C yˆ = a + bxA + cxB where xA = 1 if in treatment A, and = 0 if not in treatment A xB = 1 if in treatment B, and = 0 if not in treatment BA family consisting of three people-P₁, P2, and P3-belongs to a medical clinic that always has a physician at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic exactly once and is randomly assigned to a station. One experimental outcome is (1, 2, 1), which means that P₁ is assigned to station 1, P₂ to station 2, and P3 to station 1. Using the outcomes for the chance experiment, identify outcomes in each of the following events. Let A be the event that all three people go to the same station, B be the event that all three people go to different stations, and C be the event that no one goes to station 3. (a) BC BC = {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 3, 1), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 3), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3)} {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1),…
- V Based on advancements in drug therapy, a pharmaceutical company is developing Resithan, a new treatment for depression. A medical researcher for the company is studying the effectiveness of Resithan as compared to their existing drug, Exemor. A random sample of 414 depressed individuals is selected and treated with Resithan, and 191 find relief from their depression. A random sample of 557 depressed individuals is independently selected from the first sample and treated with Exemor, and 213 find relief from their depression. Based on the medical researcher's study can we conclude, at the 0.05 level of significance, that the proportion p₁ of all depressed individuals taking Resithan who find relief from depression is greater than the proportion p₂ of all depressed individuals taking Exemor who find relief from depression? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in…The table shows the earnings (in thousands of dollars) of a random sample of 11 people with bachelor's degrees and 10 people with associate's degrees. At α=0.05 is there enough evidence to support the belief that there is a difference in the earnings of people with bachelor's degrees and those with associate's degrees? Complete parts a through f. Bachelors - 48 34 54 58 44 41 75 28 58 26 25 Associates- 25 28 48 32 48 42 42 34 38 36 critical value and test stat?A researcher is interested in the effect of listening to music on knowledge acquisition. She randomly selects 82 students from her Introduction to Psychology course to participate. Half of the selected students is asked to listen to music of their choice while studying for an exam and the other half is asked not to listen to any music while studying. After the exam, she computes the exam scores and obtains results presented below. Can the researcher conclude that there is an effect of listening to music on knowledge acquisition? Conduct the appropriate statistical test (two-tailed) with a = .05. Music group (m) O dependent samples t test one sample t test independent samples t test X 97.3 m S = 9.0 m Based on the information provided above, which statistical test seems most appropriate? z test No music group (nm) X = 93.1 nm S nm = 10.0
- A production manager is interested to know if the distribution of defective items produced by threemachines are homogeneous. From a random sample of 200 items produced by machine I it wasfound that 150 items have no falt, 30 items have one fault and rest of the items have more than onefault. Of the 180 items produced by the machine II it was found that 85% items have no fault, 10%items have one fault and rest of the items have more than one fault. From a total of 220 itemsproduced by machin III, it was found that 205 items have no fault, 10 items have one fault and restof the items have more than one fault.(a) Construct the contigency table considering status of defectives in row and type of machinein column(b) What percentage items with one fault produced by each of the machine I and III?(c) Test at 5% significance level whether the distribution of defective items produced by threemachines are homogeneous or not?The next two questions go together. You cross true-breeding lines of tall, purple-flowered pea plants with short, white-flowered pea plants and find that all the F₁ offspring are tall and purple-flowered. When an F₁ is self-pollinated, you get 109 tall, purple: 19 tall, white: 22 short, purple: 10 short, white plants. Your null hypothesis is that the offspring fit a model of two independently-assorting loci, with tall dominant to short and purple dominant to white, and that deviations from the 9:3:3:1 ratio are due to chance. Fill out the table to calculate the x2 value for the data. For the last column, where decimals are involved, write your answer to one decimal point (e.g. 5.2). Phenotype Observed Expected o-e (o-e)² Tall, purple (o-e)²/e 109 Tall, white 19 Short, 22 purple Short, 10 white Total 160 160 How many degrees of freedom are there? [Select] What is the appropriate critical value of the x2 statistic at p=0.05? [Select] What is the p-value range (for example 0.5-0.1 or…A researcher is interested in the effect of listening to music on knowledge acquisition. She randomly selects 82 students from her Introduction to Psychology course to participate. Half of the selected students is asked to listen to music of their choice while studying for an exam and the other half is asked not to listen to any music while studying. After the exam, she computes the exam scores and obtains results presented below. Can the researcher conclude that there is an effect of listening to music on knowledge acquisition? Conduct the appropriate statistical test (two-tailed) with a = .05. Music group (m) X 97.3 m s = 9.0 m Which of the following values is the value of the test statistic in this analysis? 1.49 2.00 4.41 2.10 No music group (nm) X = 93.1 nm S nm = 10.0
- A doctor is trying to decide if a patient has one of three diseases d1, d2, or d3. Two tests are to be carried out, each of which results in a positive (P) or a negative (N) outcome. There are four possible test patterns PP, PN, NP, and NN. National records have indicated that, for 10,000 people having one of these three diseases, the distribution of diseases, and test results are as shown below: Please find the image below What is the probability that a randomly selected patient has the 2nd disease d2? What is the probability that a randomly selected patient has a test result of NP? If a randomly selected patient gets a test result of NP, what is the probability that the patient has the third disease d3?Researchers are interested in whether the presence of another person influences one’s level of self-reported stress when performing a public speaking tasks. Participants performed the public speaking task on three different occasions. Once in the presence of a friend who provided support, another time in the presence of a stranger who provided support, and a third time alone, without any support7 and 8 please