a) Let X₁, X₂, X3,... X, be a random sample of size n from population X. Suppose that X-N (0,1)and Y =-√n.i) Show that the standard score of the sample mean X, is equal to Y.ii) Show that the mean and variance of the random variable Y are 0 and 1, respectiviii) Show using the moment generating function technique that Y is a standard normal randomvariable. a) Let X₁, X₂, X3,... X, be a random sample of size n from population X. Suppose that X-N (0,1)and Y =-√n.i) Show that the standard score of the sample mean X, is equal to Y.ii) Show that the mean and variance of the random variable Y are 0 and 1, respectiviii) Show using the moment generating function technique that Y is a standard normal randomvariable.

It is given that X follows N(θ, 1), then E(X) = θ and V(X) = 1, And the moment genarating function…

Answered: Let X₁, X₂, X3,..., X be a random…

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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Let Y1, Y2,...,Yn be independent random variables with Y; Poisson(A;). Show that the sum of these random variables S has a Poisson distribution with rate paramcter A = di.
The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9180 observations, the sample mean interval was x1 = 62.6 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,872 observations, the sample mean time interval was x2 = 70.0 minutes. Historical data suggest that σ1 = 8.91 minutes and σ2 = 11.78 minutes. Let μ1 be the population mean of x1 and let μ2 be the population mean of x2. (a) Compute a 95% confidence interval for μ1 – μ2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
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The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9520 observations, the sample mean interval was x1 = 62.8 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,117 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that ?1 = 8.98 minutes and ?2 = 12.83 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 90% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
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