A time series {yt} follows an MA(2) model: Yt = 2 + Ut +0.54t-1 + 0.4ut-2. Assume that ut is a white noise series with a mean of O and a variance of 2. Please calculate Var(yt) (i.e. the varianc
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A time series {yt} follows an MA(2) model: Yt = 2 + Ut +0.54t-1 + 0.4ut-2. Assume that ut is a white noise series with a mean of O and a variance of 2. Please calculate Var(yt) (i.e. the variance of) 2.96 1.41 2.82 O 1.98
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- Assume the MR model: Y = 3 + 4x1 + 5x2 + epsilon, with sigma = 5 Select the Excel command that will find P(Y < 18) when X₁ = 2 and X₂ = 1. (Note: epsilon is the random error term and sigma is the population standard deviation)What does this mean in ARMA(p q) model: However, since an ARMA model would also display decaying ACF andPACFsSuppose the log-ins to a company's computer network follow a Poisson process with an average of three counts per minute. What is the mean time between counts? What is the standard deviation of the time between counts? a. E(X) = 0.333, SDX) = 0.111 b. E(X) = 0.333, SD(X) = 0.333 Oc. NONE Od. E(X) = 3, SD(X) = 3
- REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that σ1 = 0.5 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.20 hours per night. Previous studies show that σ2 = 0.7 hour. (a) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ1 − μ2. Round your answer to two decimal places.)(b) Find (or estimate) the P-value. (Round your answer to four decimal places.) (c) Find a 98% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limitREM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults.+ Assume that REM sleep time is normally distributed for both children and adults. A random sample of n₁ = 11 children (9 years old) showed that they had an average REM sleep time of x₁ = 2.7 hours per night. From previous studies, it is known that ₁ = 0.6 hour. Another random sample of n₂ = 11 adults showed that they had an average REM sleep time of x₂ = 2.0 hours per night. Previous studies show that σ₂ = 0.7 hour. (a) Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (0) What is the level of significance? State the null and alternate hypotheses. O Hoi Hy M₂ (ii) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately…REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 11 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that σ1 = 0.7 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.00 hours per night. Previous studies show that σ2 = 0.6 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 10% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference μ1 − μ2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.) test statistic critical value…
- REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that σ1 = 0.6 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that σ2 = 0.8 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)X is a point estimator of: Select one: a. Population mean b. Sample mean c. Sample variance d. Population varianceREM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 8 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that ?1 = 0.9 hour. Another random sample of n2 = 8 adults showed that they had an average REM sleep time of x2 = 2.00 hours per night. Previous studies show that ?2 = 0.6 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (a) What is the level of significance?State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 = ?2; H1: ?1 < ?2 H0: ?1 = ?2; H1: ?1 > ?2H0: ?1 < ?2; H1: ?1 = ?2 (b) What sampling distribution will you use? What assumptions are you…
- 1 find the first four moments of the binomial distribution 9. Ifx is a binomial variate with parameters 6 and 2 about origin.The occurrence of traffic accidents at an intersection may be modeled as a Poisson process. Based on historical records the average rate of accidents is once every 6 years. Part 1 What is the probability that there will be no accidents at the intersection for a period of 3 years? (Answer correct to 3 decimal places.) number (rtol=0.001, atol=D0.001) Part 2 Suppose that in every accident at the intersection, there is a 5% probability of fatality. Based on the above Poisson model what is the probability of one traffic fatality at this intersection in a period of 3 years? (Answer correct to 3 decimal places.) Hint: Note that here you need to find the mean rate of fatalities per year, first. number (rtol=0.001, atol=D0.001)Using R, run simulated annealing for a 2 parameter cauchy distribution (with beta constrained to 0.1, so only a single parameter alpha remains) and the negative log-likelihood curve for alpha has serval optima. show a summary graph of the values of alpha visited during the algorithm and how they relate to the position of the optima. data of the cauchy distribution are x<- c(-4.20, -2.85, -2.30, -1.02, 0.70, 0.98, 2.72, 3.50)