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...
1. Two normal random variables X and Y are jointly distributed with Var(X) 25 and Var(Y) 1600. It is known that P(Y>80| X = 50) 0.1 and P(Y 22 X 40) 0.7886 (1) What is the correlation coefficient between X and Y? (2) What is the expected value of Y given X 50?
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...
Let Xi, x,, ,X, be independent random variables with mean and variance σ . Let Y1-Y2, , Y, be independent random variables with mhean μ and variance a) Compute the expected value of W b) For what value of a is the variance of W a minimum? σ: Let W-aX + (1-a) Y, where 0 < a < 1. Let Xi, x,, ,X, be independent random variables with mean and variance σ . Let Y1-Y2, , Y, be independent random...
You are given three independent random variables: X, Y, and Z. The expected values of each are 0, and the variances of each are 1. Let U1 =Y + Z and let U2 = X – Y. (a) What are the variances of U1 and U2? (b) What is Cov(U1, U2)? (c) Combining your answers to (a) and (b), what is the correlation coefficient p between U1 and U2?
Two random variables are jointly distributed with joint pdf given by: = 0, elsewhere a) Find the value of K? b) Find the best LMMSE of Y. what is the MMSE error in this case? c) Find the best MMSE estimator of Y? d) What is minimum mean square error of Y given that x -1 Two random variables are jointly distributed with joint pdf given by: = 0, elsewhere a) Find the value of K? b) Find the best...
6.72 Let Y =X+N where X and N are independent Gaussian random variables with different variance and N is zero mean. (a) Plot the correlation coefficient between the “observed signal” Y and the “desired signal” X as a funtion of the signal-to-noise ratio (b) Find the minimum mean square error estimator for X given Y (c)Find the MAP and ML estimators for X given Y (d) Compare the mean square error of the estimators in parts a, b, and c.
Saudi Electronic University 2011 CSTS-SEU-KSA 1. Find the Linear correlation coefficient between variables x and y for the following data: 4 4 9 2. Obtain the Regression equation of y on x using the data given in Question
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...
(b) X and Y are two uniformly distributed random variables between 0 and 1. Z is a function of X and Y. Find the probability density function (pdf) of Z for the followings: Z- IX-Y i.e, absolute difference) Be sure to draw the pdf of Z and label the function, domain, and range. (5 marks) (c) The following results summarize an attempt to build a home-to-work trip generation model. Write down the answer for the ten blanks according to the...
please lease solve all questions. 2. Consider the following two variables X and Y: 4 a. (2 pts) Find the mean of X, and mean of Y b. (2 pts) Find the standard deviation of X, and standard deviation of Y C. (3 pts) Find the covariance between X and Y d. (2 pts) Find correlation coefficient between X and Y and comment on your answer. 3. The following table shows a random sample of 100 hikers and the areas...