Each of 150 newly manufactured items is examined and the number of scratches per item is recorded (the items are supposed to be free of scratches), yielding the following data: Number of scratches per item 1 3 4 6 7 Observed frequency 18 37 42 30 13 7 2 1 Let X be the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter u. Knowing the E(X) = µ for the Poisson random variable X, then E(X) would be: a b d.
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- answer item 4 onlySuppose Y1, Y2, Y3 is an i.i.d sample of size n=3 from a Poisson population distribution with Y,+2Y2+3Y3 1 mean e > 0. Let be 6. unbiased estimator for Othen MSE(e) is Select one: а. 70 18 b. 70 С. d. 140 61. The proportion of rats that successfully complete a designed experiment (e.g., running through a maze) is of interest for psychologists. Denote by Y the proportion of rats that complete the experiment, and suppose that the experiment is replicated in 10 different rooms. Assume that Y₁, Y2,..., Y₁o are i.i.d. Beta random variables with a = 2 and 3 = 1. Recall that for this Beta model, the pdf is (2y if 0 0.9). otherwise.
- Let x be a random variable that has a distribution with mean μ = 150 and standard deviation σ = 15.3. For samples of size n = 36 the sampling distribution of i s with mean = and standard deviation = .A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.Find the corresponding z-score for a sample of n = 16 and M = 38 taken from a population with a mean of μ= 40 and σ = 8.
- answer the following question number 3 with all partsSuppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Suppose we obtain n observations from a sinusoid contaminated by Gaussian noise: X = A· sin(2 · T· f·k+¢) + Wk, k = 1, 2, ...,n, %3D where Wg are independent identically distributed (iid) Gaussian random variables with mean o and variance o?. The frequency f and phase o are known constants, while A is an unknown constant. Find the maximum likelihood estimator for A. Show all work.Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Let L be the random variable for the length of time, in years, that a person will remember an actuarial statistic. For a certain popula- tion, L is exponentially distributed with mean 1/Y, where Y has a gamma distribution with a = 4.5 and 3 = 4. Find the variance of L.A random sample of size 36 from a population with known variance, o = 9, yields a sample mean of x = 17. Find ß, for testing the hypothesis H,: u = 15 versus H1 : =16. Assume a 0.05. %3D %3DSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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