Let Y, represent the ith normal population with unknown mean #, and unknown varianceof for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, fromthe ith population with sample mean Y, and sample variance S? =(₁-₁)².j=1(e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument.(f) Find a (1-a) x 100% confidence interval for of(g) For non-zero constants a's, what is the distribution of U₂ = a₁Y₁-0₂Y₂? State allthe relevant parameters of the distribution.

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Answered: Let Y, represent the ith normal…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The following table was generated from the sample data of 10 newborn babies regarding the weight of the mother at birth, the weight of the father at birth, and the weight of the baby at birth. The dependent variable is the weight of the baby, the first independent variable (x)) is the mother's weight, and the second independent variable (x2) is the father's weight. Coefficients Standard Error t-Stat p-value Intercept 9.739264 1.337045 7.284173 0.000165 Mother's Weight -0.929448 0.137340 - 6.767476 0.000261 Father's Weight 0.717791 0.159475 4.500951 0.002795 Copy Data Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places. Answer E Tables E Keypad How to enter your answer (opens in new window) Keyboard Shortcuts X + X2
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If P(A) = 0.52, P(B) = 0.45 and P(A u B) = 0.76, then P(B | A) = (Enter a number between 0 and 1, using two decimal points)
Suppose that the general fertility rate, g f rt , is following an AR(1) process shown in the image below A) if y1<1, what is the expression for the mean and variance of g f t rt showing any assumptions that were made . b) suppose that Var (€|gfrt-1)= as shown in the image below. explain why you may not obtain a best linear unbiased estimator of y0 and y1 by estimating (3) using OLS.
4) A set of measurements is given as follows. X = [0.1, 0.3, 0.8, 12,4, 7,9] We want to approximate the source of this data with Gamma distribution, i.e., X~Gamma(a, B). For Gamma distribution, the mean and variance can be found from the below equations. a Hx a o = Find the parameters of Gamma distribution to fit the data. Come up with two other distributions that you think are good representation of this data. Justify your answer.
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3. Assume that the distribution of the length X of male spider is N(ux,o}) and the length Y of female spiders is N(µy,o?), and X and Y are independent. Construct approximated 95% one-sided confidence intervals for o? /o? when n = m = 30, and = 0.4399 and S? = 1.4100.
A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…
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The following table consists of one student athlete's time, x, (in minutes) to swim 2,500 yards and the student's heart rate, y, (beats per minute) after swimming on a random sample of 5 days: Athlete's Time (x) Heart Rate (y) x2 y? ху 33.43 145 34.89 150 35.12 125 37.27 143 36.56 138 ТОTAL 1. Compute for the value of Pearson's r. 2. Interpret the value of r.
A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…

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