Question 22X follows a continuous uniform distribution{}}0f(x)=Applying the central limit theorem with a random sample of size n-64 results in which of thefollowing expressions?OX-51OX-0.254√3O X-10ㅎOX-5if 3 ≤ ≤7otherwise√6Time Purring30 Minutes24/7 ProcteCalL

Answered: Image /qna-images/answer/e7495396-2ced-4ed7-a96e-9ca9edb120af.jpg

Answered: X follows a continuous uniform…

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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QUESTION 11: "In (2 less than X less than 8), X is a " continuous random variable discrete random variable no variable constant QUESTION 12: Discrete data are made continuous by using class boundaries class intervals cumulative frequency probability QUESTION 13: Find the expectation of a random variable X? if X = 7, 9, 10, 11, 12, and P(X) = 0.2, 0.25, 0.3, 0.15, 0.1 respectively" 11.5 4.5 9.5 14.5 QUESTION 14: Find the Mean of f(x), where f(x) = 5X+5. The probability distribution of a random variable X ; if X = 12, 14, 15, 16, 17, and P(X) = 0.2, 0.25, 0.3, 0.15, 0.1 respectively" 11 37.5 42 77.5 QUESTION 15: A small voting district has 110 female voters and 90 male voters. A random sample of 10 voters is drawn. What is the probability exactly 7 of the voters will be female? 0.75 0.51 0.224 0.1665
CHAPTER 7 , QUESTION 1 /3 Central Limit Theorem for SumsSuppose random samples of n=42n=42 are collected from an unknown distribution with the properties μ=53μ=53 and σ=3σ=3. Determine the mean of ΣXΣX. Determine the standard deviation of ΣXΣX. (Include 6 decimal places.)
Which of the following statements about the Central Limit Theorem (CLT) is correct?1. The CLT states that the sample mean is always equal to the population mean.2. The CLT states that the sampling distribution of the sample mean is approximately normal for large sample sizes (n > 30).3. The CLT states that the sample mean is equal to the population mean, provided that n > 30.4. The CLT states that the sampling distribution of the population mean is approximately normal, provided that n > 30. In a distribution plot, if the mean is equal to the median, is the possible shape of the distribution skewed to the right, skewed to the left, or symmetric? If batteries have lives that are normally distribute with mean 2, 800 hours and standard deviation 400 hours, using the 68-95-99.7 rule to approximate the percentage of batteries having a life less than 3, 600 hours.
Which of the following are specified by the central limit theorem? a. the mean of a specific sample from the distribution of sample means b. the mean of the distribution of sample means c. the shape of the distribution of sample means d. the variability for the distribution of sample means
For which of the following situations would the central limit theorem not imply that the sample distribution for ?¯x¯ is approximately Normal? a population is Normal, and we use samples of size ?=6n=6 . a population is Normal, and we use samples of size ?=50n=50 . a population is not Normal, and we use samples of size ?=50n=50 . a population is not Normal, and we use samples of size ?=6n=6 .
1. Suppose that X1, Xn is an iid random sample from a distribution with pdf f(x; sigma) = 1/2 * (sigma) * e ^ (- |x| / sigma) - infinity0 0(a) Find the method of moments estimator (MME) of \sigma. Hint: See the example in lecture notes. (b) Find the maximum likelihood estimator (MLE) of \sigma. Hint: See the example in lecture notes. (c) Use central limit theorem to find the large - sample asymptotic distribution of the MLE in part (b). (d) Suppose 10 independent observations were taken from the given distribution: (0.5, 0.8, 2.2, 1.6, 2.0, 2.8, 1.5, 0.9, 2.5, 1.8). What is the numerical value of the MLE? What is the numerical value of the estimated standard deviation (standard error) of the MLE?
The following is a sufficient condition, the Laplace–Liapounoff condition, for the central limit theorem: If X1, X2, X3, ... is a sequence of independent random vari-ables, each having an absolute third moment ci = E(|Xi − μi|3) and if lim n→q[var(Yn)]− 32 ·ni=1ci = 0 where Yn = X1 + X2 +···+ Xn, then the distribution of the standardized mean of the Xi approaches the stan-dard normal distribution when n→q. Use this condi-tion to show that the central limit theorem holds for the sequence of random variables of Exercise 7.
Consider a random sample X1, … , Xn from the pdff (x; u) = .5(1 + (THETA)x) -1 <= x <= 1where -1 <= theta <= 1 (this distribution arises in particlephysics). Show that theta = 3X is an unbiased estimator oftheta. [Hint: First determine mu = E(X) = E(X).]
Which of the following is NOT a condition that ALWAYS has to be satisfied to apply the Central Limit Theorem to the sample mean? a) The sample size must be larger than 30 b) There are no obvious outliers in the sample if the sample size is less than 30 c) There are no extreme outliers in the sample if the sample size is at least 30. d) The sample observations are independent.
The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following: a. E(x) P(x=1) c. P(x= 4) d. P(x6) e. P(2x5)
1. Let X have a gamma distribution with α > 1. Show thatE [1/X] = 1/[θ*(α −1)]
For each of the following situations determine if the Central Limit Theorem can be applied: (Type Y for Yes and N for No) a. In the world populations, normal body temperature follows a normal distribution with mean = 98.6 degrees F and a standard deviation of 0.6. The mean body temperature will be determined for a randomly selected group of 14 individuals. Answer:Blank 1 b. Mean number of songs on a student’s IPOD will be determined for a randomly selected group of 10 students. In the college population, it is known that the number of songs on a student’s iPod is skewed to the left. Answer:Blank 2 c. Now assume that you are randomly selecting 800 students to determine the mean number of songs on the iPod. Answer:Blank 3

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X follows a continuous uniform distribution {} 0 f(x)= Applying the central limit theorem with a random sample of size n-64 results in which of the following expressions? OX-5 SA OX-0.25 4√3 OX-10 if 3 ≤ a ≤7 otherwise OX-5