Consider drawing samples of sizen = 12 from U(0,12) Consider estimators for the population variance. One such estimator is the familiar s'. When you draw such a sample, what is E(s') ? Another is the sample range r, where r = ymax - Ymin When you draw such a sample, what is E(r) ? Hint: E(y max) = 144/13 using Theorem 3.10.1
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Consider a real random variable X with zero mean and variance σ2X . Suppose that wecannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and{Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe information…If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameter
- Q2C. Considering the following MA(3) process: y_t = u_t − 0.7u_(t-1) − 0.2u_(t-2) + 0.4u_(t-3) Where u_t is a white noise process with variance equal to 1. What is the value epsilon_k = cov(y_t,y_(t-k)) for k = 0? Provide the correct answer along with the working steps and underlying assumptions used to calculate the value of epsilon_k = cov(y_t,y_(t-k)) for k = 0.Suppose a linear model y=β0+β1xy=β0+β1x is fit to a sample data set, and a test of the null hypothesis H0:β1=0H0:β1=0 against an alternative hypothesis HA:β1≠0HA:β1≠0 is performed; a PP-value of 0.4203 is obtained. Which of the following scatter plots depicts the data set on which this model was fit and the hypothesis test was performed?A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.33. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.37. At α=0.01, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below. (a) Write the claim mathematically and identify H0 and Ha. A. H0: σ2≤1.33 (Claim) Ha: σ2>1.33 B. H0: σ2≠1.33 Ha: σ2=1.33 (Claim) C. H0: σ2≥1.33 Ha: σ2<1.33 (Claim) D. H0: σ2=1.33 (Claim) Ha: σ2≠1.33 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is(are) enter your response here. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Choose the correct statement below and fill in the corresponding answer boxes. A. The…
- You are conducting quality control for a company that manufactures LED displays. The factory you are assessing is supposed to have a manufacturing defect rate of 1 in 100 LED displays. As part of your assessment, you want to verify this defect rate by analyzing a random sample of LED displays. You are planning to randomly sample 1500 displays from this factory and observe how many of them contain manufacturing defects. Let Zi be equal to 1 if the i’th display has a defect and 0 otherwise, for i = 1,...,1500. (a) What is the statistic that you will use to estimate the defect rate for this factory? How do you compute it using Z1, Z2, . . . , Z1500? (b) Assuming that the true defect rate for this factory is in fact 1 in 100 displays, can we approximate the sampling distribution of the statistic that you selected in part (a) using a normal distribution? Please state and check the requirements for applying the approximation, and identify the mean and standard deviation of the normal…Note- bolded quiz have already answered A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5-9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L.*8.31 What are the appropriate null and alternative hypotheses to compare the means of the two groups? *8.32 What is the appropriate test procedure for the hypotheses in Problem 8.31? *8.33 Carry out the test in Problem 8.32 using the criticalvalue method. *8.34 Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke. *8.35 Assuming…
