Suppose the random variable, X, follows a geometric distribution with parameter (0<0 <1). Let X₁, X₂, X, be a random sample of size n from the population of X.(d) Find the method of moments estimator (mme) of 0.(e) Show how the mle of 0 is related to its mme. Explain if it is always true.(f) Verify ifX, is a sufficient statistic for 8 or not.(g) Justify if = is an unbiased estimator for 6.

X~Geom(p)Note: According to the Bartleby guidelines expert solve only one question and maximum three…

Answered: Suppose the random variable, X, follows…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let x represent the number of mountain climbers killed each,year. The long-term variance of x is approximately o Suppose that for the past 12 years, the variance has been s = 118.3. = 136.2 Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2 Find a 90% confidence interval for the population variance. (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom?
Suppose the random variable, X, follows a geometric distribution with parameter 0 (0< 0 < 1). Let X₁, X2, X, be a random sample of size n from the population of X. (e) Show how the mle ofis related to its mme. Explain if it is always true. (f) Verify if X, is a sufficient statistic for or not. (g) Justify if = = is an unbiased estimator for 6.
If the coordinates of point A (x, y) are two random variables with a normal distribution with zero mean(average) variance 4, it is desirable to calculate the probability that the distance of this point from the origin of the coordinates is less than 1.
Suppose a simple random sample of size n = 40 is obtained from a population with μ = 68 and o = 17. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x <71.1). (c) Assuming the normal model can be used, determine P(x270.1). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What must be true regarding the distribution of the population? A. Since the sample size is large enough, the population distribution does not need to be normal. OB. The population must be normally distributed. OC. The population must be normally distributed and the sample size must be large. OD. There are no requirements on the shape of the distribution of the population. Assuming the normal model…
The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9180 observations, the sample mean interval was x1 = 62.6 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,872 observations, the sample mean time interval was x2 = 70.0 minutes. Historical data suggest that σ1 = 8.91 minutes and σ2 = 11.78 minutes. Let μ1 be the population mean of x1 and let μ2 be the population mean of x2. (a) Compute a 95% confidence interval for μ1 – μ2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
A simple random sample without replacement was used to select 5 clusters from a population of 29 clusters. From each selected sample cluster simple random sampling without replacement was used to select samples of secondary units. For this data find an estimate of the population total and the population mean along with their estimated variances. clmemb clsize yval [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] [13,] [14,] [15,] [16,] [17,] [18,] [19,] [20,] [21,] [22,] [23,] [24,] [25,] [26,] [27,] [28,] [29,] [30,] [31,] [32,] [33,] 1 20 46.07 20 45.54 20 43.07 1 1. 1 20 49.29 1 20 44.35 1 20 45.21 2 33 44.11 2 33 42.19 2 33 44.42 2 33 40.05 2 33 43.88 2 33 47.45 2 33 40.41 2 33 43.24 3 22 35.42 3 22 35.46 3 22 36.34 3 22 35.25 4 40 38.67 4 40 34.73 4 40 39.28 4 40 35.26 4 40 39.84 4 40 40.32 4 40 40.03 4 40 38.15 4 40 38.69 4 40 39.38 18 47.48 18 44.78 5 18 44.37 18 44.97 5 18 49.20
Suppose a simple random sample of size n= 39 is obtained from a population with µ = 62 and o = 19. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x<65.2). (c) Assuming the normal model can be used, determine P(x2 63.2). Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2). (a) What must be true regarding the distribution of the population? O A. The population must be normally distributed. O B. The population must be normally distributed and the sample size must be large. O C. Since the sample size is large enough, the population distribution does not need to be normal. O D. There are no requirements on the shape of the distribution of the population. Assuming the normal…
The useful life of a concrete built on the seashore has a Weibull distribution of parameter scale δ> 0 year and power β = 2. Determine a) The half life of concrete EXb) The variance VXc) The probability that the concrete lasts more than 10 years; P (X> 10)
Suppose a simple random sample of size n=10 is obtained from a population with μ=68 and σ=19. Answer a-c (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x<71.1). (c) Assuming the normal model can be used, determine P(x≥69.2).
TRUE OR FALSEa. When the assumptions of distributions are met, the parametric tests are more powerful than non-parametric testsb. In Poisson distribution, the mean is equal to its variance c. The Main objective of Statistical inference is to make inferences about the population-based n the whole set of population values d. The Variable X defined X~N(0,1) is called the Standard Normal Distribution e. Welch Test for testing two population means does not assume that the variances are equal
The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9520 observations, the sample mean interval was x1 = 62.8 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,117 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that ?1 = 8.98 minutes and ?2 = 12.83 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 90% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
A proton emitter produces proton beams with changing kinetic energy that is uniformly distributed between three and eight joules. Suppose that it is possible to adjust the upper limit of the kinetic energy (currently set to eight joules). • What is the mean kinetic energy? What is the variance of the kinetic energy? What is the probability that a proton beam has a kinetic energy of exactly 3.5 joules? a. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a continuous distribution O b. E(X) = 5, V(X) = 1.33, probability is zero (0) because X has a uniform distribution O c. NONE O d. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a uniform distribution

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