4. [-14 Points] DETAILS (4pt) The variance of random variable X is 1 and the variance...
(4pt) The variance of random variable X is 4 and the variance of random variable Y is 16. The correlation coefficient between the two random variables X and Y is 0.9. (a) (1pt) Find the covariance between X and Y. (b) A new random variable Z is given by Z = 5x + 1. Find the covariance between X and Z. (1pt) Find the covariance between Y and Z. (2pt)
explain as much as possible! thanks! (4pt) The variance of random variable x is 1 and the variance of random variable Y is 16. The correlation coefficient between the two random variables X and Y is 0.9. (a) (1pt) Find the covariance between X and Y. (b) A new random variable Z is given by Z = 5x + 1. Find the covariance between X and Z. (1 pt) Find the covariance between Y and Z. (2pt)
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. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
A random variable X is normally distributed with a mean of 121 and a variance of 121, and a random variable Y is normally distributed with a mean of 150 and a variance of 225. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable below. Av-218 (Type an integer or a decimal.) σ (Type an integer or a decimal.)
2. (-13 Points) DETAILS TANFIN12 8.3.002. The probability distribution of a random variable x is given. MY NOTES 12 -2 0 2 4 PCX = ) 0.3 0.1 0.2 0.2 0.2 Compute the mean, variance, and standard deviation of X. (Round your answers to two decimal places.) mean variance standard deviation The probability distribution of a random variable X is given. 1 View 2 3 4 P(X = x) 0.3 0.4 0.2 0.1 Compute the mean, variance, and standard deviation...
7. X is a random variable with a mean of 2 and a variance of 3, and Y is a random variable with a mean of 4 and a variance of 5, and the covariance between X and Y is -3. Define (a) Find the expected value of W. b) Find the variance of W
Let the variance of random variable X be 3, the variance of Y be 12, and the variance of Z be 9, and let X, Y , and Z be uncorrelated. Find V ar(4 − 2X + 3Y − 10Z).