Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6.1, Problem 13E
Consider a random sample X1,..., Xn from the
where −1 ≤ θ ≤ 1 (this distribution arises in particle physics). Show that
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
X1,X2,...,Xn are i.i.d. random variables from N(0,θ) distribution. Here, θ= σ2 >0is the variance of the distribution, and is an unknown parameter. Find the MLE of θ(no need tocalculate the second derivative).
Suppose X1, . . . , Xn are i.i.d. from a continuous distribution with p.d.f.
fθ(x)=1/2(1+θx)if −1≤x≤1,
where θ ∈ [−1, 1] is an unknown parameter.
(a) Find E(X1).(b) Find the MME for θ.
(c) Compute the variance of your MME from part (a).
Suppose X1, . . . , Xn are i.i.d. from a continuous distribution with p.d.f.
fθ(x) = 1/θ if 0 ≤ x ≤ θ,
where θ > 0 is an unknown parameter.
(a) Find E(X1)
(b) Find the MME for θ.
(c) Compute the variance of your MME from part (a).
Chapter 6 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 6.1 - The accompanying data on flexural strength (MPa)...Ch. 6.1 - The National Health and Nutrition Examination...Ch. 6.1 - Consider the following sample of observations on...Ch. 6.1 - The article from which the data in Exercise 1 was...Ch. 6.1 - As an example of a situation in which several...Ch. 6.1 - Urinary angiotensinogen (AGT) level is one...Ch. 6.1 - a. A random sample of 10 houses in a particular...Ch. 6.1 - In a random sample of 80 components of a certain...Ch. 6.1 - Each of 150 newly manufactured items is examined...Ch. 6.1 - Using a long rod that has length , you are going...
Ch. 6.1 - Of n1 randomly selected male smokers, X1 smoked...Ch. 6.1 - Suppose a certain type of fertilizer has an...Ch. 6.1 - Consider a random sample X1,..., Xn from the pdf...Ch. 6.1 - A sample of n captured Pandemonium jet fighters...Ch. 6.1 - Let X1, X2,..., Xn represent a random sample from...Ch. 6.1 - Suppose the true average growth of one type of...Ch. 6.1 - In Chapter 3, we defined a negative binomial rv as...Ch. 6.1 - Let X1, X2,..., Xn be a random sample from a pdf...Ch. 6.1 - An investigator wishes to estimate the proportion...Ch. 6.2 - A diagnostic test for a certain disease is applied...Ch. 6.2 - Let X have a Weibull distribution with parameters ...Ch. 6.2 - Let X denote the proportion of allotted time that...Ch. 6.2 - Let X represent the error in making a measurement...Ch. 6.2 - A vehicle with a particular defect in its emission...Ch. 6.2 - The shear strength of each of ten test spot welds...Ch. 6.2 - Consider randomly selecting n segments of pipe and...Ch. 6.2 - Let X1,..., Xn be a random sample from a gamma...Ch. 6.2 - Prob. 28ECh. 6.2 - Consider a random sample X1, X2,, Xn from the...Ch. 6.2 - At time t = 0, 20 identical components are tested....Ch. 6 - An estimator is said to be consistent if for any ...Ch. 6 - a. Let X1,.., Xn be a random sample from a uniform...Ch. 6 - At time t = 0, there is one individual alive in a...Ch. 6 - The mean squared error of an estimator is MSE ()...Ch. 6 - Prob. 35SECh. 6 - When the population distribution is normal, the...Ch. 6 - When the sample standard deviation S is based on a...Ch. 6 - Each of n specimens is to be weighed twice on the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardFind the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.arrow_forwardLet X1,...,Xn ∼ iid Pois(θ), and we wish to estimate φ = Pθ(X = 0) = e−θ. Consider Yi = I (Xi = 0). Show that ∑ni=1 Yi follows a Bin(n, φ) distribution. (d) Using Y1 , . . . , Yn find an unbiased estimator for φ. (e) Is the estimator in (d) the MLE for φ?arrow_forward
- Suppose X1, . . . , Xn are i.i.d. from a continuous distribution with p.d.f. fθ(x) = 1/θ if 0 ≤ x ≤ θ, where θ > 0 is an unknown parameter. (a) Find E(X1) ALREADY ANSWERED (b) Find the MME for θ. (c) Compute the variance of your MME from part (a). I have asked this question multiple times and this last time it asked for clarification of whether it was MME (Methods of Moments Estimator) or MLE (Maximum Likelyhood Estimator). It calls for MME not MLE.arrow_forward2. Let X₁,..., Xn be iid observations from a pdf defined by 0 f(x|0) = 0 0. (1+x)¹+0¹ Find a complete sufficient statistic.arrow_forwardLet fo(X) = {(1/7) 0 X₁, X₂,..., Xn be i.i.d. samples with pdf 0 0, Otherwise. Assume: 1 Estimator 1 is Ô = 2 X. 2 Estimator 2 is Ô = X(n). Answer the following questions: Q1 Are these estimators unbiased? Q2 Are these estimators consistent?arrow_forward
- If 1. If for >0 the energy of a pdf is E(x)=r, find the variance. (A) 1 (B) 2 (C) 1/2 (D) Undefined (E) 0arrow_forward9. Let Y1, Y2,..., Yn constitute a random sample from the pdf given by f (y) = 2 (0 – y) for 0 < y <0. %3D Find an estimator for 0 by using the method of moments. estimator =arrow_forward2 Consider an SRS 2Yi3;=, from the pdf fy(y;o)= -(y-0) for y≤ [0,00). ye e What is an unbiased estimator involving Ymin?arrow_forward
- 2. Let dt Find the average %3D value of f on the interval [o, 1arrow_forward• If the joint PDF of X and Y is shown as follows: fxx(x, y) = e-(x+y) Find the following: 12) The marginal distributions of X and Y. 13) Find the value of P[X | 0 < Y < 5].arrow_forward1. Let X have the pdf f(x) = B-lexp{-x/B}, 0 < xarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License