a)Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X followsan exponential distribution with parameter 0 and Y = ===1 X₁.nb)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 thestatistic Y is given byY =X1 X2 X3₁²+X3² +X5²i) 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?

Note: According to Bartleby guidelines expert solve only one question and maximum three subpart of…

Answered: a) Let X₁, X2, X3,..., Xn 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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The weights of beagles (dogs) have approximately a normal distribution with u = 17.1 pounds and a standard deviation of o = 1.8 pounds. Suppose that we randomly select n = 64 beagles and measure their weights in pounds. Let X be the random variable representing the mean weight of the selected beagles. Let Xtot be the random variable representing the total weight of the selected beagles. a) About what proportion of beagles have weights between 17 and 18 pounds? b) About what proportion of beagles have weights greater 20 pounds? c) About how many of the 64 sampled beagles have weights less than 16.5 pounds? (nearest integer) d) About how many of the sampled beagles have weights between 17 and 18 pounds? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot? g) What is the probability that 17 1100? f) Copy your R script for the above into the text box here.
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
3. If Z is a random variable having the standard normal distribution, find i. P(Z - 1.08) iii. P(-1.90
5. Let (Xi, Yi), i 1, 2, ,n, be a random sample from a bivariate normal distribution. Find the joint distribution of (X,Y).
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…
The weight of a male bald eagle has approximately a normal distribution with mean ?= 7.4 pounds and a standard deviation of ?= 1.6 pounds. Suppose we take a random sample of n=64 male bald eagles. Let X̄ be the random variable representing the mean weight in pounds of the 64 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 84 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 64 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 64 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X̄ (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the…

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