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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- X and Y are independent random variables with variances 2 and 3.Find the variance 3X+4Y.Prove that Var(aX + b) = a²Var(X) for a random variable X and scalars a and b, where Var represents variance.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 y
- 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 falseX 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 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.
- 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)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?
- 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.(TRUE / FALSE) For two random variables, X and Y, Var(X+Y) = Var(X)+Var(Y) if X and Y are uncorrelated.Suppose a car's city miles per gallon rating can be determined by the car's weight. The means and standard deviations of these variables and the correlation coefficient between them are reported in the following table. Determine the coefficients of the least squares line for predicting a car's miles per gallon rating from its weight. Report the equation of this line. 2 decimals for "a" and 5 decimals for "b"
