Let X and Y be independent uniform random variables on (0,1). (a) Find the variance of Z₁ = min(X, Y). (b) Find the variance of Z₂ max(X, Y).
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- Let X and Y be independent uniform random variables on (0,1). a) Find the variance of Z1=min(X,Y). b) Find the variance of Z2 = max(X,Y).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 yThe profit for a new product is given by Z = 3X-Y -5. X and Y are independent random variables with Var(X) = 1 and Var(Y) =2 what is the variance of Z?
- Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is p(1-p)The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanationLet X and Y be independent random variables with means x,y and variances o, oy. Find an expression for the correlation of XY and Y in terms of these means and variances.
- Consider (Y, X) values in a population as (8, 2), (9, 3), (10, 3), (12, 5), (14, 6), (16, 6) and (17, 8). Draw all possible samples from this population and compute Ratio estimator for each sample. Show that the ratio estimator is a biased estimator of population mean but has smaller mean square error as compared with the variance of mean per unit estimator.A random variable Y has a uniform distribution over the interval (8,, e,). Derive the variance of Y. Find E(Y)? in terms of (e,, e,). E(Y)? = Find E(Y) in terms of (e,, e,). E(Y) = Find V(Y) in terms of (8,, e,). V(Y) =Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. Find the mean and variance of U = 2X - 3Y. . Find the mean and variance of V = XY.
