3. Suppose we have a random variable X with mean a new random variable Y as...
If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) = .8, find Cov(2x-Y, X + 5Y). If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) =...
We have a random variable, X. Using the variable, we construct a new variable Y, defined below: Y = 3X+5. Calculate the mean and variance of Y in terms of X. (i) E(Y) (ii) Var(Y)
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
. 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....
Suppose we have a sample of observations for the pair of random variable (X, Y) in the following 2 x2 Show that the odds ratio can be estimated by ad/bc and derive an estimate of the variance of this estimator Suppose we have a sample of observations for the pair of random variable (X, Y) in the following 2 x2 Show that the odds ratio can be estimated by ad/bc and derive an estimate of the variance of this estimator
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?
Random variable X has mean Ux=24 and standard deviation σx =6. Randon variable Y has mean Uy =14 and standard deviation σY = 4. A new random variable Z was formed, where Z=X+Y. What can we conclude about X, Y, and Z with certainty? That is, which one is true?
Suppose that X is a standard normal random variable with mean 0 and variance 1 and that we know how to generate X. Explain how you would generate Y from a normal density with mean μ and variance σ"? That is, given that we already generated a random variate X from N(0,1), how would you convert X into Y so that Y follows N (μ, σ 2)?
(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)
Suppose random variables X and Y are related as Y=7X+3. Suppose the random variable X has mean 1, and variance 1. What is the expected value of X+Y ? Solution provided is 11. How was this obtained?