(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)
4. [-14 Points] DETAILS (4pt) The variance of random variable X is 1 and the variance of random variable Y is 4. The correlation coefficient between the two random variables X and Y is 0.2. (a) (1pt) Find the covariance between X and Y. (b) A new random variable Z is given by Z = 2X + 1. Find the covariance between X and Z. (1pt) Find the covariance between Y and Z. (2pt)
Page 13 of 13 15. (3 points each) Let X be a random variable with a mean of 10 and a variance of 4. Let Y be a random variable with a mean of 8 and a variance of 3. The covariance of X and Y is Oy 0.2. Let W-6Y-4X + 2 a. Find E(W) b. Find Var(W)
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 =...
5. Suppose X is a normally distributed random variable with mean μ and variance 2. Consider a new random variable, W=2X + 3. i. What is E(W)? ii. What is Var(W)? 6. Suppose the random variables X and Y are jointly distributed. Define a new random variable, W=2X+3Y. i. What is Var(W)? ii. What is Var(W) if X and Y are independent?
. Suppose that Y is a normal random variable with mean µ = 3 and variance σ 2 = 1; i.e., Y dist = N(3, 1). Also suppose that X is a binomial random variable with n = 2 and p = 1/4; i.e., X dist = Bin(2, 1/4). Suppose X and Y are independent random variables. Find the expected value of Y X. Hint: Consider conditioning on the events {X = j} for j = 0, 1, 2. 8....
Thank you Assume that Y is a 3 × 1 random vector with mean vector ,y = μ and covariance matrix ΣΥΥ-σ2 . I. Assume that e is an independent random variable variable with zero mean and variance ф2 . Derive the mean and variance for W-2 1 Y + 5. Derive the covariance matrix between W and Y 6. Derive the correlation matrix between Wand Y. 7. Derive the variance covariance matrix for V- W Y, i.e., derive
3. Let X be the height of Zebras, assume the X is a random variable with mean 10 and variance 20. Suppose Y is be the weight of Zebras, assume the Y is a random variable with mean 10 and variance 40. Let E(XY)-80 (a) Find the covariance and correlation between X and Y. Find the covariance and correlation between aX + b and cY + d. a,b,c, and d are unknown constants. Your answer can depend on them. (b)...
Assume X is a normal random variable with mean 20 and variance 16, and Y is a Gamma random variable with parameters 5 and 2. In addition X and Y are independent. Construct a box with length L = [X], width W = 2|X|, and height H = Y. Let V be the volume of the box. Calculate the expected value E[V]?
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)