find the correlation between X and Y
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Suppose that the two dimensional random variable (X. Y) has p.d.f. given by f(x. y) = ke^-y .0 < x< y < 1 . elsewhere Find the correlation coefficient rxy
we need to find the correlation between X and Y.
4.he sample correlation coefficient between X and Y, rxy Sx/Sx S where S-the covariance between X and Ys Σ(X-XM) (-Yu)/ n-1 Sx the standard deviation of X and Sy the standard deviation of Y I) If the covariance is positive, the correlation coefficient must be positive: True or False? ii) If the covariance is negative, the correlation coefficient must be positive: True or False? a) ii) The correlation coefficient must lie between 0 and 1. True or False? v)lf the...
Suppose the two-dimensional random variable (X, Y ) is uniformly distributed over the triangle of the figure.a) What is f.d.p.c. of (X,Y). Calculate P(0 < X ≤ 1, Y > 1). Make a graphic sketch of the regionthat you used to calculate the probability. b) Determine the marginal distributions. (X, Y ) are independent?c) Find E[X] ,V AR[X], E[Y ] e V AR[Y ];d) Determine the conditional distributions. Use the conditionals to answer : (X, Y ) areindependent?e) Calculate E[XY ],...
Suppose X andY are two random variables withE[X]=1,Var(X)=4,E[Y]=−1,Var(Y)=4,andCov(X,Y)=1. Find: (a) correlation between X and Y . (b) Var(X −Y).
The random variable x has a p.d.f. given by: f(zfor 0 2 Find the UPPER quartile, Q3 O 0.5 O 0.375 0.75 1.5 Given the following joint probability distribution of X and Y 10.0450.08l10.1 Then X + Y takes on values 2,3,4,5, and 6. Build the probability distribution for Z = X + Y by matching the appropriate probability to each value of Z. 1. 0.16 2. 0.215 3. 0.27 4. 0.045 5. 0.315
3, X and Y are two jointly Ga a. b. th G (μ, μ., σ. σ2y, py). ussian random variables WI What is the "most likely" value of X given Y? If Z = X+Y, find the correlation coefficient between Z and Y assuming for this part that the means of X and Y are zeros. 3, X and Y are two jointly Ga a. b. th G (μ, μ., σ. σ2y, py). ussian random variables WI What is the...
2. Let the following data be given where X is the independent variable and Y is the dependent variable Find the correlation coefficient r a. a and B,onpfrom the sample for the model: b. Estimate +tx and the actual data Y where ε is the random error between the fitted model f by Y write the linear equation P=" dr-h Predict the value of P when x = 8 c. d. 2. Let the following data be given where X...
4.2 The Correlation Coefficient 1. Let the random variables X and Y have the joint PMF of the form x + y , x= 1,2, y = 1,2,3. p(x,y) = 21 They satisfy 11 12 Mx = 16 of = 12 of = 212 2 My = 27 Find the covariance Cov(X,Y) and the correlation coefficient p. Are X and Y independent or dependent?
Random variable (20) Z X+Y is a random variable equal to the sum of two continuous random variables X and Y. X has a uniform density from (-1, 1), and Y has a uniform density from (0, 2). X and Y may or may not be independent. Answer these two separate questions a). Given that the correlation coefficient between X and Y is 0, find the probability density function f7(z) and the variance o7. b). Given that the correlation coefficient...
1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for 0 〈 x 〈 2. r for 0<< f(x) = 0 otherwise. Let Y - X (2 - X). First determine the c.d.f. of Y, then find its p.d.f. (Hint: when computing c.d.f., plotting the function Y- X(2 - X) which may help. )