Let X and Y be random variables, and a and b be constants. ???? a)  Show that Cov [aX,bY] = abCov [X,Y] . b)  Show that if a > 0 and b > 0, then the correlation coefficient between aX and bY is the same as the correlation coefficient between X and Y . c)  Is the correlation coefficient between X and Y unaffected by changes in the units of X and Y ?

Q: Let X and Y be statistically independent random variables with Var(X) = 4 and Var(Y) = 10. We do not…

A: The provided information is as follows:. and  are independent random variables..

Q: A computer while calculating correlation coefficient between two variables X and Y from 25 pairs of…

A: The question is about correlation.Given :No. of pairs ( n ) = 25Incorrect pairs : ( 6,14 ) and ( 8,6…

Q: 2. Let X and Y be random variables such that V(X) = V(Y). Show that Cov(X + Y, X - Y) = 0.

A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

Q: Is there a linear correlation between x and y? Use α = 0.01.   a.) Yes, because the correlation…

A: Given: The data points are as below x y 2 9 8 1 8 2 8 3 9 1 9 2 9 3 10 1 10 2…

Q: 3. The table below mmHg for a sa ic, x Diastolic, y 5 89 B 85 5 83

A: Given, Sample Systolic  (x) Diastolic (y) 1 136 89 2 118 85 3 116 83 4 126 84 5 122 74…

Q: Suppose that X ~ U (0, a) where a is a constant. Let Y = X². Calculate the %3D correlation…

A: We have given a uniform distribution and we have to find the correlation coefficient between the…

Q: Let Xi and Yi be random variables with Var(Xi) = σx2 and Var(Yi) = σy2 for all i ∈ {1, . . . , n}.…

A: It is given that: varxi=σx2varyi=σy2 and xi and yi are independent and corrxi,yi=ρ

Q: What does a correlation coefficient of -1 indicate? a) There is a perfect positive linear…

A: 1) Option (C) ✔️  There is a perfect negative linear correlation  Explanation :- A correlation of…

Q: Suppose that X and Y are unknown with E(X) = 20, Var (X) = 4 , E(Y) = 12, and Var (Y) = 16. In…

A: It is given that, E(X) = 20, Var (X) = 4 and E(Y) = 12, and Var (Y) = 16 and E(XY) = 248

Q: Suppose that Y1 and Y2 have correlation coefficient py, ,Y, and for constants a, b, c and d let W, =…

A:

Q: Let X and Y be random variables with Var (X₂) o and Var(Y₂) o for all ie {1,...,n}. Assume that each…

A: (a) The covariance between Xi and Yi is given by: Cov(Xi, Yi) = E[(Xi - E[Xi])(Yi - E[Yi])] Since…

Q: Estimate the correlation coefficient for the following graph. O

A: Note: If the data points distributed in random manner, then there is no correlation. That is, r=0.…

Q: We have the following information about the random variables X and Y: |x=2, |y=−1 , ox = 0.25, c X…

A: a)It is given that, .

Q: 1. Consider X = Z,Y = Z² with Z = N(0, 1). Which of the following statements is correct? (a) X and Y…

A: Note: According to Bartleby guidelines expert solve only one question and rest can be reposted.

Q: ox²= 3, oy² = 5, oxy = 2, Z=2Y - 4X – 2 a. Determine the variance of Z.

A:

Q: a) ∑xy b)∑x2 c)∑y2 d)∑x e)∑y vi) Calculate the product moment correlation coefficient. vii)…

A: Given: n=9

Q: Q1-Q5: a) Find the value of the line ar correlation coefficient r b) Find the critical values ofr…

A: Note: Since the question has 5 subparts and its not mentioned here which parts have to be solved, so…

Q: 3.a. Suppose Var(X1) = 2.25, Var(X2) = 2.56, and Cov(X1, X2) = -0.25. Find the correlation p of X1…

A: Correlation (X1,X2)= cov(X1,X2)/√V(X1)*V(X2) = -0.25/√2.25*2.56 = -0.10417