Suppose the random variables X and Y are inde lent and identically distributed. Let Z =aX +Y. If the correlation coefficient between X and Z is1/3 , then what is the value of the constant a ? Exercises1. Suppose that X1 and X2 are random variables with zero mean and unitvariance. If the correlation coefficient of X1 and X2 is –0.5, then what is thevariance of Y = =k2Xk ?Lk=12. If the joint density of the random variables X and Y isif (x, y) E { (x,0), (0, -y)|x, y = -2, –1, 1,2}f(x, y)otherwise,3. Suthe random variables X and Y are indelent and identicallydistributed. Let Z = aX +Y. If the correlation coefficient between X andZ is , then what is the value of the constant a ?

3. Given that X and Y are independent and identically distributed. That is, the correlation between…

Answered: uppose the random variables X and Y are…

uppose the random variables X and Y are inde lent and identically distributed. Let Z =aX +Y. If the correlation coefficient between X and Z is1/3 , then what is the value of the co

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...

See similar textbooks

Related questions

Q: Use the following table to find the linear correlation coefficient between x and y

A: Given data, X Y X*Y X*X Y*Y 1 3 3 1 9 1 1 1 1 1 2 1 2 4 1 4 2 8 16 4 3 3 9 9 9 2 4 8…

Q: A fair coin is tossed three times (consecutively). If X is the number of heads of the first shot and…

A: GivenX represent the number of heads in first toss.So X can take values {0,1} Y represents the…

Q: A random variable X is normally distributed with a mean of 81 and a variance of 81, and a random…

A: Given variable: W = 8X - 3Y For X: Mean = 81 Variance = 81 For Y: Mean = 160 Varinace = 256…

Q: The scatterplot shows the relationship between two random variables X and Y. - If r=0.15 then what…

A: Solution

Q: A motion picture industry analyst is studying movies based on epic novels. The following data were…

A: From the given information, Let x1 denotes the first year box office receipts of movies. x1…

Q: If X, Y and Z are uncorrelated and independent variables with the same variance o and zero mean.…

Q: Two random variables have the regression equations : 3 X+ 2Y- 26 = 0 6X+ Y- 31 = 0 Find the mean…

A: Regression equation are used to predict the future values based on the independent variable that act…

Q: A large sample of data is collected in order to study the relationship between the two variables X…

A: A large sample of data is collected in order to study the relationship between the two variables X…

Q: An urn contains 10 white balls and 8 red balls. 2 balls are selected at random. Let X denote the…

A: The number of balls in the urn is given as follows:White=8; Red=2The variables are given as…

Q: A perfect straight line sloping downward would produce a correlation coefficient equal to: O A. -1…

A: Given that ; A perfect straight line sloping downward would produced a correlation…

Q: Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 10 8 13 11 9.13 9…

A: Given,

Q: 15. If x₁=Y1+ y2, X2 = y2 + Y3, x3 = y3+y₁, where y₁, y2 y3 are correlated variables each of which…

Q: Find the value of the linear correlation coefficient r. Two different tests are designed to measure…

A: Given data, X Y X*Y X*X Y*Y 23 49 1127 529 2401 25 53 1325 625 2809 28 59 1652 784 3481…

Q: A fair coin is tossed three times (consecutively). If X is the number of heads of the first shot and…

A: It is an important part of statistics . It is widely used .

Q: Show that the coefficient of determination is indeed equal to the square of the linear correlation…

Q: A researcher obtains a Pearson correlation of r = 0.60 for a sample of n = 6 pairs of X and Y…

A: From the provided information, Pearson correlation (r) = 0.60 (pairs of X and Y scores) Sample size…

Q: 2. The following data were obtained in a study of the relationship between the weight and chest size…

Q: When the correlation coefficient (r) is zero, we can say: Select one: to. the variables are not…

A: When the correlation coefficient (r) is zero, we can say: Select one: to a . the variables are not…

Q: Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the…

A: From provided information, Data of Row 1 and Row 2 is, Row 1 10 22 36 47 50 64 77…

Q: A random variable X is normally distributed with a mean of 121 and a variance of 121, and a random…

A: The mean of the random variable W=7X+6Y is, μW=E7X+6Y=7μX+6μY=7×121+6×170=847+1020=1867 Thus, the…

Q: Assume that the computed correlation between x and y is -0.13. Suppose we define a new variable s=…

A: Given that the correlation between x and y is -0.13. s=-x and t=y+6

Q: Arandom variable X is normally distributed with a mean of 121 and a variance of 121, and a random…

Q: W = 6X + 3Y (Do not round.) (Do not round.)

A: X and Y are normally distributed random variables μx=81var(X)=81 μy=200var(Y)=400r=0.5

Q: A random variable X is normally distributed with a mean of 100 and a variance of 500, and a random…

A: Given,E(x)=100V(x)=500E(y)=200V(y)=400r=-0.5

Q: Σx = 58, Σy = 358, Σx2 = 422, Σy2 = 12,944, and Σxy = 2145. Test the claim that the population…

Q: For these data, find the SSx, SSy, SP, and Pearson correlation coefficient, r.

A: Given: XY16025835545710230

Q: Suppose that a random voltage V supplies a random current I through a constant resistive load. What…

A: The correlation between the random variables V and I is given by ρV, I=CovV, IVarV·VarI.

Q: Let the sample correlation coefficient be -0.5. We can conclude that Select one: a. x and y are not…

A: It is given that the sample correlation coefficient is –0.5.

Q: Use the following table to find the linear correlation coefficient between x and y X 2 3 4 1 2 2 3 2…

Q: Two independent variables x, and x, are with means 5 and 10 and variances 4 and 9. If u = 3x, +4x,…

Q: Suppose that given a particular dataset of (x, y) pairs, the correlation coef- ficient (r) of the…

A: The correlation coefficient defined the relationship between two quantitative variables. The value…

Q: Q1) Test a correlation relationship by using Pearson Superman coefficients. 2 2 2 1 1 1 y 3 X 4 2 2…

Q: A researcher interested in the correlation between family size X annual income Y and parental…

A: It is required to find the correlation coefficient between annual income and parental education…

Q: Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values…

A: Let us calculate the correlation coefficient r by letting row 1 as x values and row 2 as y values.…

Q: at random and with replacement from this population. Let X, Y, and Z be the values of the ndividuals…

A: To find correlation between u= 2x+3y v= 3x+2y-3z x, y and z are independent random variable

Q: A researcher collected data on people's heights and their shoe sizes from 500 people (N=500). Then,…

Q: A value of r close to 0 indicates what type of linear correlation between the two variables? a.…

A: A value of r close to 0 indicates that either variables have no correlation or weak correlation.

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

Suppose the random variables X and Y are inde lent and identically distributed. Let Z =aX +Y. If the correlation coefficient between X and Z is1/3 , then what is the value of the constant a ?

Exercises
1. Suppose that X1 and X2 are random variables with zero mean and unit
variance. If the correlation coefficient of X1 and X2 is –0.5, then what is the
variance of Y = =k2Xk ?
Lk=1
2. If the joint density of the random variables X and Y is
if (x, y) E { (x,0), (0, -y)|x, y = -2, –1, 1,2}
f(x, y)
otherwise,
3. Su
the random variables X and Y are inde
lent and identically
distributed. Let Z = aX +Y. If the correlation coefficient between X and
Z is , then what is the value of the constant a ?

Definition Definition Statistical measure used to assess the strength and direction of relationships between two variables. Correlation coefficients range between -1 and 1. A coefficient value of 0 indicates that there is no relationship between the variables, whereas a -1 or 1 indicates that there is a perfect negative or positive correlation.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Continuous Probability Distribution$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

29) Two variables are measured on a random sample of n = 23. The sample data results ina sample correlation of 0.393. If you fit a simple regression model to the data, whatvalue would the coefficient of determination (or R-squared) take on?A) 0.627B) 0.393C) 0.154D) 0.000E) 0.296
he data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 39inches. Is the result close to the actual weight of 126 pounds? Use a significance level of 0.05. Chest size (inches) 44 41 41 55 51 42 Weight (pounds) 213 206 176 309 300 178 Critical Values of the Correlation Coefficient r n α=0.05 α=0.01 NOTE: To test H0: ρ=0 against H1: ρ≠0, reject H0if the absolute value of r is greater than the critical value in the table. 4 0.950 0.990 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590 19…
1. Find the correlation coefficient 2. Find the p-value
Suppose a study finds that the correlation coefficient relating job satisfaction to salary is r=1. Which of the following are the proper conclusions? I. High salary causes high job satisfaction. II. Low salary causes low job satisfaction. III. There is a very strong association between salary and job satisfaction. I only IIl only I and Il only I, Il and III O O
For the data given in the table below, find the linear correlation coefficient r and the least-squares regression line x y ------- 1 18 3 13 3 9 6 6 7 4 -------
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 4.3), (2, 6.4), (4, 7.8), (6, 11.7), (8, 16.4)}
A history instructor has given the same pretest and the same final examination each semester. he is interested in determining if there is a relationship between the scores of the two tests. he computes the linear correlation coefficient and notes that it is 1.15. what does the correlation coefficient value tells the instructor? a. there is a strong positive correlation between the test b. there is a strong negative correlation between the test c. the history instructor has made a computational error d. the correlation is something other than linear
Assume the random variable X has a standard deviation of 4, the random variable Y has a standard deviation of 5 and the two random variables have a correlation of 0.6. What is the covariance of X and Y?
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 X are independent. b. the mean and variance of Z assuming X and X are not independent and their correlation coefficient is 0.50.
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.
Let X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The covariance of x and y is 0.35. Let Z=4X – 5Y+2. What is the mean and variance of Z?