1. Suppose a \( X \) value is produced by a random process that has a mean of 1 and a variance of 9, while a \( Y \) value is produced by a random process that has a mean of 9 and a variance of 1. Let \( Z = 3X - 2Y \). Compute: a. the mean and variance of \( Z \) assuming \( X \) and \( Y \) are independent. b. the mean and variance of \( Z \) assuming \( X \) and \( Y \) are not independent and their correlation coefficient is 0.50.

1) Given that E(X)=1, Var(X)=9, E(Y)=9 and Var(Y)=1. Here Z=3X-2Y. For any two random variables X…

Answered: 1. Suppose a X value is produced by a…

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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B.13. Table B-6 gives data on the number of new business incorporations (Y) and the number of business failures (X) for the United States from 1984 to 1995. a. What is the average value of new business incorporations?And the variance? b. What is the average value of business failures? And the variance? c. What is the covariance between Y and X? And the correlation coefficient? (X) + var (Y) sr= -0.8 (X+Y) 2X = 16, s2Y = 9Y = 3X2 + 2Y = ax + bY = X>4Y = 0.6X-4 Y = 3X +2 E(X) = 8 and var (X) = 4 E(XY) = a 4X=1 a 2 Y = 1 XIYi f(XI, YI) X = 20 NUMBER OF NEW BUSINESS INCORPORATIONS (Y) AND NUMBER OF BUSINESS FAILURES (X), UNITED STATES, 1984-1995 YEAR Y X 1984 634,991 52,078 1985 664,235 57,253 1986 702, 738 61,616 1987 685,572 61, 111 1988 685,095 57,097 1989 676,565 Source: Economic Report of the President, 2004, Table B-96, p. 395. TABLE B-6 d. Are the two variables independent? e. If there is correlation between the two variables, does this mean that one variable causes the other…
The weights (in pounds) of 6 vehicles and the variability of their braking distances (in feet) when stopping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface? Use α=0.01. Weight, x 5920 5370 6500 5100 5890 4800 Variability in 1.76 1.91 1.50 braking distance, y EEE Click here to view a table of critical values for Student's t-distribution. Setup the hypothesis for the test. Ho: P Ha: P 0 0 1.86 1.62 1.67 M
6.In simple linear regression, the sample correlation coefficient between the input variable and the output variable, and the estimated slope parameter : a.Must have the same sign (negative, zero, or positive) b.May have opposite signs c.Must have opposite signs d.Neither of the above
Ensure the RaceResults worksheet is active, then use the FREQUENCY function to calculate the frequency distribution of the race results in column D. Place your results in the range G4:G9. Enter a function in cell F22 to calculate the correlation between age (Columns C) and race time (Column D). Enter a function in cell G22 to calculate the covariance between age and race time. Enter a function in cell H22 to calculate the variance of the ages in the data set. Note this is a sample of data not a population. Enter a function in cell 122 to calculate the standard deviation of the ages in the data set.
Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.
The mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. You are now being told they are independent. Find the value of each requested parameter A. The mean of T= -3x +20 is ___ B. The mean of W= Y - X is ___ C. The variance of D = X - 2Y is ___
Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. a. Identify the independent and dependent variables. b. In a sentence, state the null hypothesis being tested. c. Using symbols, state the null and alternative hypotheses. d. Determine the critical region using a one-tailed test with alpha = .05. e .Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). f. State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). g. Based on your analysis, is there a relationship between the drug and attention span?
Suppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incoming students based on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at the university and gathers their freshman year GPA data and the high school SAT score reported on each of their college applications. He produces a scatterplot with SAT scores on the horizontal axis and GPA on the vertical axis. The data has a linear correlation coefficient of 0.481202. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1495.716802 Sx = 109.915203 y freshman year GPA y = 3.260911 Sy 0.492802 r = 0.481202 slope = 0.002157 Determine the y-intercept, a, of the least-squares regression line for this data. Give your answer precise to at least four decimal places. a =
Consider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then: a. All points lie in a straight line with a slope of -1. b. All points lie in a straight line with an unknown negative slope. c. All points do not lie in a straight line but the best fitting regression line has a slope of -1 d. There is a strong positive relationship between the two variables.
If X has a mean μ and variance σ and Y = aX+b where a and b are constants: Find the mean, variance, and correlation coefficient between X and Y.

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