Assume I observe 3 data points x1, x2, and x3 drawn independently from the same unknown probability. Given a model M, I can calculate the likelihood for each data point as Pr(x1 | M) = 0.5, Pr(x2 | M) = 0.1, and Pr(x3 | M) = 0.2. What is the likelihood of seeing all of these data points, given the model M: Pr(x1, x2, x3 | M)?
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Assume I observe 3 data points x1, x2, and x3 drawn independently from the same
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- Suppose a different family purchases a 2,500 square foot house, and also plans to undertake extensions that will increase the total size of the house by 500 square feet. Again, use the results in column (1), and assume the house has a pool, is in excellent condition, but does not have a view (which will not change after the extensions). Without performing any further calculations, what are you able to conclude about the expected impact of the extensions on this house? a. Both the estimated dollar increase and the estimated percentage increase in price would be the same as for the house described in previous question. b. The estimated percentage increase in price would be the same as for the house described in previous question, but the estimated dollar increase would be higher. C. Both the estimated dollar increase and the estimated percentage increase in price would be higher than for the house described in previous question. d. The estimated percentage increase in price would be the…A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory, the studio randomly selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for each movie. The results of the survey are as follows. Do the data substantiate the studio's belief that dramas will draw a larger crowd on average than comedies at α = 0.05? Let dramas be Population 1 and comedies be Population 2. Assume that the population variances are approximately equal. Box Office Revenues (Millions of Dollars) n x S Drama 14 150 50 Comedy 11 120 30 Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory, the studio randomly selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for each movie. The results of the survey are as follows. Do the data substantiate the studio's belief that dramas will draw a larger crowd on average than comedies at α = 0.05? Let dramas be Population 1 and comedies be Population 2. Assume that the population variances are approximately equal. Box Office Revenues (Millions of Dollars) Drama Comedy n x S 14 150 50 11 120 30 Copy Data Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho M₁ M₂ = 0 Ha:μ₁-1₂. .0
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- The proportion of people in a given community who have Covid-19 infection is 0.005. A test is available to diagnose the disease. If a person has Covid-19, the probability that the test will produce a positive signal is 0.009 . If a person does not have the Covid-19, the probability that the test will produce a positive signal is 0.01. What is the probability that the test will generate positive signal? Which model/rule will best be good for solving the above problem and why? Comment on the types of events you see in the problem and name them.A teacher believes that students who study more than four hours for her tests will do better than students who do not study for her tests. To test this belief, the teacher recruited 16 students and randomly assigned them to two groups: G1: a group of n1=8 students that studied more than four hours for her test, and G2: a group of n2=8 students that did not study for her test. The following are the data from G1, who studied more than four hours for the test: n1=8 M1=85 s1=5 (this is the standard deviation of the sample, dividing the sum of squares by n1) The following are the data from G2, who did not study for the test: n2=8 M2=75 s2=4 (this is the standard deviation of the sample, dividing the sum of squares by n2) Perform a t-test by answering the questions below. Use an alpha-level of α=.05. 0. Using formulas from Section 4, compute the estimates of the population variances, est. σ12 and est. σ22 (from s1 and s2 above). 1. What is the research…A student stated: “I fail to see why the response function needs to be constrained between 0 and 1 when the response variable is binary and has a Bernoulli distribution. The fit to 0, 1 data will take care of this problem for any response function.” Comment.
- SpgZ.5 points A dependent t-test study and an independent t-test study both produced a t statistic with df = 10. How many individuals participated in each study? 12 for dependent and 12 for independent 12 for the dependent and 11 for independent 11 for dependent and 11 for independent 11 for dependent and 12 for independentA researcher investigates whether cold medication effects mental alertness. It is known that scores on a standardized test containing a variety of problem-solving tasks are normally distributed with = 64 and = 8. A random sample of n = 16 teenage and a sample of n = 25 adults are given the drug and then tested. On average, the teenagers scored and average of ? = 58 and the adults scored and average of M = 65.5.a. Are the data sufficient to conclude that the medication significantly reduces mental alertness in teenagers? Test with = .01.b. Are the data sufficient to conclude that the medication significantly increases mental alertness in adults? Test with = .01.