b) Let X₁, X₂,..., X and Y₁, Y₂, ..., Ym be random samples from populations with moment generating25functions Mx, (t) = 3t+t² and My, (t) = (¹²5, respectively.i) Find the sampling distribution of the statistic W = X₁ + 2X₂ − X3 + X₁ + X5.ii) What is the value of the sample size n, if P[Σ₁(X;¡ − X)² > 68.3392] = 0.025?iii) What is the value of the sample size m, if P(|Ỹ – µy| ≥ 10) < 0.04?

Answered: Image /qna-images/answer/55d8020a-dd8f-491e-9531-a05980b9e5e8.jpg

Answered: i) Find the sampling distribution of…

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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In each situation, find the value of the standardized statistic for the sample mean, and indicate whether the standardized statistic is a t-statistic or a z-statistic. (Round your answer for part (a) to three decimal places.) (a) x 175, μ = 170, s = 21, n = 4 standardized statistic = ; ---Select--- (b) x = 175, µ = 170, σ = 20, n = 4 standardized statistic = ---Select--- (c) x = 162, μ = 170, s = 10, n = 25 standardized statistic = ---Select---
For a population with o = 12, how large a sample is necessary to have a standard error that is less than 2 points? n >?
For a population with a = 12, how large a sample is necessary to have a standard error that is less than 4 points? n > ?
The central limit theorem states that the sampling distribution of sample means has a mean equal to the population -- mean mean mean divided by the population standard deviation mean divided by the population standard deviation standard deviation standard deviation standard deviation divided by the square root of N.
A simple random sample of size n=50 is obtained from a population with a mean of 46 and a standard deviation of 7. Does the population need to be normally distributed for the sampling distribution of x bar to be approximately normally distributed? Why? What is the sampling distribution of x bar?
2.Given a random sample of size n = 29, from a normal distribution, find k such that: a) P(-k < T < 1.313) = 0.88 b) P(-k < T < k) = 0.99 c) P(-2.286 < T < k) = 0.685
10
4. Let X denote the mean of a random sample of size n from the distribution N(μ, 10) and P(x - 1²/ < μ< * + ²) = O A A. 176 C. 20 = 0.964, then the value n of is equal to B B. 13
when a population is uniformly distributed (flat), is the sampling distribution of xbar for random samples of 2 observations roughly normal, strongly skewed, or triangular?
Suppose x has a distribution with mean 22 and standard deviation 16. If a random sample of size n=36 is drawn find p(22<×<24)
a) Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = ===1 X₁. n b) i) Show that y follows a chi-square distribution with 2n degrees of freedom. ii) What is the value of the sample size n, if P(Y > 20.4831) = 0.025? iii) What is the value of sample size n, if P(|Y - 2n| <40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X1 X2 X3 ₁²+X3² +X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?

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i) Find the sampling distribution of the statistic W = X₁ + 2X₂ −X3 + X4+X5- ii) What is the value of the sample size n, if P[Σ₁(X¡ − X)² > 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Ỹ - µyl ≥10) <0.04?