D. Suppose that X,, X2, ... , X10 be a random sample from N(0,1).Find a statistic that has the following distributions:1) X² (5)2) F4,63) t(9)4) F5,5Explain your answers by using theorems and/or proofs.

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Answered: D. Suppose that X1, X2, ... , X10 be a…

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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5. Let X1, X2, . ,Xn be i.i.d. samples distributed according to Geo(q). Consider the sample mean X = 1EX; as an estimator for the mean u = E[X;]. (a) What is the value of u in terms of q? (b) What is the bias of the estimator? Show explicitly by using the linearity of expectation. What is the variance of the estimator? What is its standard error? Write the expressions in terms of q, n. (d) What is the mean square error of the estimator? Write the expression in terms of q, n.
25. Let X, and X, be independent normal random variables, X,~ N(H1, of), and let Y, = X, and Y, = X1 + X2. %3D (a) Show that Y, and Y, are bivariate normal. (b) What are the means, variances, and correlation coefficient of Y, and Y,? (c) Find the conditional distribution of Y, given Y, = y1. Hint: Use Theorem 5.4.8. %3D
dataset x = (x1, … , xn ) has sample variance of 0 when (n≥2 ). prove that all the data points are in fact equal.
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 70.0 kg and standard deviation ? = 7.6 kg. Suppose a doe that weighs less than 61 kg is considered undernourished. (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 45 does should be more than 67 kg. If the average weight is less than 67 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 45 does is less than 67 kg (assuming a healthy population)? (Round your answer to four decimal places.)(d) Compute the probability that x< 71.8 kg for 45 does (assume a healthy population). (Round your answer to four decimal places.)
Suppose that x is a normally distributed random variable with mean 5and standard distribution is 6. Find z value corresponding to x=17.
18. Which of the following is not a characteristic of the F distribution? A) It is always right-skewed. B) It describes the ratio of two variances. C) It is a family based on one of degree of freedom. D) It is always positive.
A manufacturer of semiconductor devices takes a random sample of 100 chips and tests them, classifying each chip as defective or non-defective. Let X, 0 if the chip is non-defective and X; = 1 if the chip is defective. The sample fraction defective is X, +X, +---+ X, 100 What is the sampling distribution of the random variable "P?
12 q5
9. Carboxy- hemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood (Reference: A Manual of Laboratory and Diagnostic Tests by F. Fischbach). Let x be a random variable rep- resenting percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n-12 blood tests given to a heavy smoker gave the following results (percentage of carboxyhemoglobin in the blood): 9.1 9.5 10.2 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 Where = 10.49 and s = 1.36. A long-term population mean u -10% is considered a health risk. However, a long- term population mean above 10% is considered a clinical alert that the person may be asymptomatic. We will investigate the claim: the data indicate that the population mean percentage is higher than 10% for this patient? Use a = 0.05. a. Find the test statistic. b. Find the critical…
only need d,e,f
From a population of 4 students, a random variable (X) is measured in terms of age and the values of X are 24, 20, 22, 18. Find the sampling distribution where n = 1 Compute for the Variance when n=1
9. Consider a random sample of size n from a Weibull distribution, X, WEI(0, ß). (a) Find a sufficient statistic for 0 with ß known, say ß = 2. (b) If ß is unknown, can you find a single sufficient statistic for ß?

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D. Suppose that X1, X2, ... , X10 be a random sample from N(0,1). Find a statistic that has the following distributions: 1) X² (5) 2) F4,6 3) t(9) 4) F5,5