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)?

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)?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

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…
Please please answer it only correct. In short explanation. I will really upvote
A student of EEE452 is assessing risk of pickpocket over 4 weeks (28 days) while commuting to NSU.Pocket money in his wallet randomly varies day to day. He observed that daily average pocketmoney is (i) 3000 Taka in first week, (ii) 1500 Taka in 2nd week (iii) 900 Taka in 3rd week and (iv) 500Taka in the last week. To reduce the risk he chooses different commuting services with differentprobability of pickpocket: on 1st week, Pathao ride (p = 1/300), on 2nd week Laguna service(p=1/75), 3rd week local town service bus (p=1/60) and on the last week he takes his own bicycle(p=1/100).a) What is his risk on the first week? (TK)b) What is his risk on the 2nd week? (TK)c) What is his risk on the last week of the month?d) What is his risk over the entire month (28 days)? (TK)e) Which commuting service should he be most careful about? Why?
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
For each Bernoulli process, find the expected number of successes: Number of trials =30 Probability of success =0.7. Number of trials =280 Probability of success =1/10. Number of trials =27 Probability of success =0.2 Number of trials =21, Probability of failure =0.8 Number of trials =49 Probability of failure =2/7
An internet provider wants to see if male and female college students spend a different amount of time online each day. In a random sample of 200 male college student shows the mean was 85 minutes with σ = 15 minutes. Another sample of 250 female college students has a mean of 81 minutes and σ = 17 minutes. Is there enough evidence to prove the claim at α = .05.
Assume that the data values in this problem come from independent populations and that each population follows a normal distribution.Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds).4.14 4.24 4.24 3.58 3.55 3.82 4.08 4.37 3.92 3.82 4.17 3.10 4.89 2.93 4.98 3.34Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.3238.
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…
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 0.99. If a person does not have the Covid-19, the probability that the test will produce a positive signal is 0.01.a) Which model/rule will best be good for solving the above problem b) Explain your answer in a)c) Comment on the types of events you see in the problemand name them.
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.