Let X and Y and Z are uncorrelated random variables with the same variance. Find the correlation coefficient between (X + Y) and (Y +Z).

Q: Determine the variance of Z.

A: Helpful formulas (i)VaX=a2VX(ii)VC=0,where c is the constant(iii)VaX+ bY=a2VX+ b2VY

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: Determine the linear correlation

A: Given : Data Let : X: X ValuesY: Y ValuesMx: Mean of X ValuesMy: Mean of Y ValuesX - Mx & Y -…

Q: Ey = 100 Ex = 850 >x- 9° = 210 п3 10 X : E(x - x) (х — 2) (у - Ў) %3 2050 = 3216.7 (10- 1)

A: Coefficient of Correlation: It is a measure of the strength of the straight line or linear…

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

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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: The regression lines between two random variables X and Y is given by 3X + Y = 10 and3X + 4Y = 12…

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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: Find the variance with solution

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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…

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

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Q: Two variables have the regression lines 3x + 2y = 26 and 6x + y = 31. Find the mean values, the…

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Q: Find the regression line relating the statistics final average to the OR final average. (c)…

A: Given: Statistics OR 86 80 75 81 69 75 75 81 90 92 94 95 83 80 86 81 71 76…

Q: Listed below are amounts of court income and salaries paid to the town justices. All amounts are in…

A: Given data represents the amounts of court income and salaries paid to the town justices.…

Q: Find the equation of the least squares line and the linear correlation coefficient for the given…

A: Given: x 2 3 4 6 8 y 6 6 8 11 18

Q: Suppose the variance of X is 95. What is the variance of .09X?

A: The objective of this question is to find the variance of a variable that has been scaled by a…

Q: Find the Covariance and the Correlation between X and Y

A: Given: n=5 The covariance and correlation are calculated as…

Q: Why might we calculate the correlation coefficient for x and y values in a scatterplot?

A: Scatter plot is use to draw a relationship between two variables.

Q: A negative value of the correlation coefficient indicates that the variables are unrelated. O true O…

A: Negative Correlation :  If the  change in the value of one variable results in the change of value…

Q: Two regression lines of a sample are X+6 Y=6 and 3X+2Y=0. Find the correlation coefficient.

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Q: X, =2, o =9, X2 =-1, ox, = 4 and Cx,x2 =-3, are transformed to new random variables Y, and Y,…

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Q: What does the square of the linear correlation coefficient measure (rxr)

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Q: A factory sorts out the number of beverage vending machines (x) and the number of beverage cans sold…

A: It is given that the factory sorts out the number of beverage vending machines (x) and the number of…

Q: (6,9),(8,15),(2,16),(10,22) What is the best estimate for the linear correlation coefficient and…

A: If we draw al line thorough scattered plot it will give us estimate approximately 0.50

Q: The command aov(x,y) can be used to calculate the correlation coefficient between x and y O True O…

A: aov(x, y) is used to find correlation between x and y  True  False

Q: A zero correlation bewteen X and Y is least likely to occur if?

A: The strength and direction of linear relationship between two variables is measured by correlation,…

Q: Find the variance

A: Given : X~N(0, 7)

Q: Suppose the scatter diagram of a random sample of data pairs (x,y) shows no linear relationship…

A: If the value of the sample correlation coefficient is 1, then there is strong positive linear…

Q: Two statistically independent ran dom have variances of Variables X and new Man- Y o² = 9 and of dom…

A: U=3X+4YV=5X-2Yand X , Y two independent random variables.

Q: Please calculate the covariance and the correlation coefficient for the two random variables and…

A: From the given information,       y           -4 0 1 3 f(x)   3 0.02 0.06 0.1 0.02…

Q: Suppose Y1, Y2 and 3Y are not correlated variables, however, have the same standard deviation. Show…

A: Given  Y1 , Y2, Y3 are independent of each other.  They have same standard deviations

Q: If covariance between X and Y variables is 10 and the variances of X and Y are respectively 16 and…

A: The objective is to find correlation coefficient