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1. Let Y₁, Y2, Y3, Y4, Ys be a random sample of size 5 from a standard normal population. Find the moment generating function of the statistic: X = 2Y₁²+ Y₂² + 3Y3² +Y4² +4Y5²

1. Let Y₁, Y2, Y3, Y4, Ys be a random sample of size 5 from a standard normal population. Find the moment generating function of the statistic: X = 2Y₁²+ Y₂² + 3Y3² +Y4² +4Y5²

MATLAB: An Introduction with Applications
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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12 -A A abc X, X² A-ay-A= Font 1. DS L -re to search Aa- - ¶ AaBbCcDc AaBbCcDc AaBbC AaBbCct AaB AaBbcct AdB Normal T No Spac... Heading 1 Heading 2 Title Subtitle Subtle 2. 3. F 5. Paragraph Let Y₁, Y2, Y3, Y4, Ys be a random sample of size 5 from a standard normal population. Find the moment generating function of the statistic: F X = 2Y₁²+ Y₂² + 3Y3² +Y4² +4Y5² Let Y₁, Y2, Y3, Y4, Ys and X₁, X2, X9 be independent and normally distributed random samples from populations with means = 2 and 2 = 8 and variances ₁2 = 5 and 022= k, respectively. Suppose that P(X-Y>10) = 0.02275, find the value of ₂² = k 6. ENGLISH (SOUTH AFRICA) Styles Suppose that Y, Y2. Ym and X1, X2, ..., X are independent normally distributed random samples from populations with means and uz and variances ² and 02², respectively. Is X-Y a consistent estimator of 2-1? Justify your answer. 14. Suppose that Y₁, Y2, Y is a random sample of size m from Gamma (a = 3, B = 8), where is not known. Check whether or not the maximum likelihood estimator & is a minimum variance unbiased estimator of the parameter. Suppose that a random sample X1, X2, X20 follows an exponential distribution with parameter p Check whether or not a pivotal quantity exixts, if it exists, find a 100 (1 - a) % confidence interval for p. Suppose that a random sample X is given by a probability density function 19°C 43 12
Transcribed Image Text:12 -A A abc X, X² A-ay-A= Font 1. DS L -re to search Aa- - ¶ AaBbCcDc AaBbCcDc AaBbC AaBbCct AaB AaBbcct AdB Normal T No Spac... Heading 1 Heading 2 Title Subtitle Subtle 2. 3. F 5. Paragraph Let Y₁, Y2, Y3, Y4, Ys be a random sample of size 5 from a standard normal population. Find the moment generating function of the statistic: F X = 2Y₁²+ Y₂² + 3Y3² +Y4² +4Y5² Let Y₁, Y2, Y3, Y4, Ys and X₁, X2, X9 be independent and normally distributed random samples from populations with means = 2 and 2 = 8 and variances ₁2 = 5 and 022= k, respectively. Suppose that P(X-Y>10) = 0.02275, find the value of ₂² = k 6. ENGLISH (SOUTH AFRICA) Styles Suppose that Y, Y2. Ym and X1, X2, ..., X are independent normally distributed random samples from populations with means and uz and variances ² and 02², respectively. Is X-Y a consistent estimator of 2-1? Justify your answer. 14. Suppose that Y₁, Y2, Y is a random sample of size m from Gamma (a = 3, B = 8), where is not known. Check whether or not the maximum likelihood estimator & is a minimum variance unbiased estimator of the parameter. Suppose that a random sample X1, X2, X20 follows an exponential distribution with parameter p Check whether or not a pivotal quantity exixts, if it exists, find a 100 (1 - a) % confidence interval for p. Suppose that a random sample X is given by a probability density function 19°C 43 12
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