Let X and Y be random variables with variances Var(X) = 1 and Var(Y ) = 2. (Note that X and Y might not be independent.) What is the maximum possible value of Var(3X − 2Y + 4)?
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- Prove that Var(aX + b) = a²Var(X) for a random variable X and scalars a and b, where Var represents variance.X and Y are independent random variables with variances 2 and 3.Find the variance 3X+4Y.R adjusts for the random errors and the number of B parameters in the model and its value is always larger than the coefficient of multiple determination. True or false
- The lines of regression of y on x and x on y are, respectively, y = x + 5 and 16x - 9y = 94. Find the variance of x if the variance of y is 16. Also, find the covariance of x and ySuppose the variance of the difference of two random variables X and Y is zero. Then, show that X = Y + c for some constant c almost surely. Also find the value of c.X and Y are random variables such that Var(X) = 4, Var(Y) = 6 and Var(X+Y) = 16. Calculate Var(a X + b Y), where a and b are arbitrary constants. The final answer is an expression.
- Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate Var(5X−7Y+17)A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1).Find its mean value and variation.
- Let X and Y be identically distributed with mean 3 and variance 25. (a) If X and Y are uncorrelated, what is the variance of X+Y? (b) If the covariance between X and Y is 7, what is the variance of X+ Y?(TRUE / FALSE) For two random variables, X and Y, Var(X+Y) = Var(X)+Var(Y) if X and Y are uncorrelated.