here are seven swans in a castle lake. With probability 1/4, each swan attracts a mate from elsewhere. After these new swans have moved in, what is the variance of the number of swans in the lake?
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- Suppose X is an outcome in throwing a fair die. Find the mean and varianceSuppose X and Y are uncorrelated random variables. Which of the following statements are true? Group of answer choices: the sample correlation for 10 data points sampled from the joint distribution of X and Y will be exactly 0. X and Y have no relationship X and Y are independent X and Y have no linear relationship3.12 Mark is deciding which route to take to work. His choices are I = the Interstate and F = Fifth Street.• P(I) = 0.44 and P(F) = 0.55• P(I AND F) = 0 because Mark will take only one route to work.What is the probability of P(I OR F)?
- In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 7% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month?Suppose you are interested in buying a new Lincoln Navigator or Town Car. You are standing on the sales lot looking at a model with different options. The list price is on the vehicle. As a salesperson approaches, you wonder what the dealer invoice price is for this model with its options. The following data are based on a random selection of these cars of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle. x 32.4 32.9 36.1 44.0 47.8 y 30.4 31.0 32.0 42.1 42.2 (b) Use a 10% level of significance to test the claim that ρ > 0. (Use 2 decimal places.) t ? critical t ? (c) Verify that Se ≈ 1.5629, a ≈ 2.5006, and b ≈ 0.8551. Se ? a ? b ? (e) Find a 95% confidence interval for y when x = 42 (thousand dollars). (Use 2 decimal place.) lower limit ? upper limit ? (f) Use a 10% level of significance to test the claim that β > 0. (Use 2 decimal places.) t ? critical t ?Bobo, the amoeba, currently lives alone in a pond After one minute Bobo will either die, split into two amoebas, or stay the same, with equal probability. Find the variance for the number of amoebas in the bond after one minute
- Three people are running for president of the student council. The polls show James has odds in favour of winning at 2:3, Rebecca has odds in favour at 7:13, and Henry has odds in favour at 1:3. Suppose that Henry withdraws and offers his support to Rebecca. Further, suppose that his supporters also switch to Rebecca. What is the probability of Rebecca winning now?In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:June is a student taking a statistics course. Unfortunately, June is not a diligent student. She does not read the textbook before or after class, does not do homework, and regularly misses class. She intends to rely on luck to pass the next quiz. The quiz consists of 10 multiple-choice question. Each question has five possible answers. Only one of the answers is correct, so the probability of choosing the correct answer is 0.20. June plans to guess the answer to each question independently. Let � be the number of correct answers on June’s quiz. What is the standard deviation of correct answers for June? Group of answer choices 8 2 1.26 1.14 None of These
- Problem Solving. Solve the following problems. No immediate rounding. Round off final answers to three decimal places. A protective enchantment which alerts the Charms professor when a death eater attacks a magical school is designed to have a 90% reliability rate. Suppose that the nine magical schools equipped with this enchantment experienced an attack from the death eaters. Define the random variable X as the number of Charms professors alerted out of nine. Assuming that protective enchantment alerts are independent 1. Write down the associated PMF of X. 2. Compute for the probability of alerting at least 7 Charms professors.. In an organization consisting of 5 women and 10 men, a committee of four individuals is to be selected at random from the 15 people. Find the distribution of the random variable, X = Number of women on the committee.
