: X = n-¹ Σr=1 Let (X, 1 ≤r ≤ n} be independent and identically distributed with finite variance, and define Xr. Show that cov(X, X, - X) = 0.
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- 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) =Suppose that X has the uniform distribution on the interval [0, 1]. Compute the variance of X.let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2. Find the mean and the variance of U= (1/2)W
- Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2 otherwise. Submit your answer in fractional form.Let X~N(0, 0'). Find the CRLB for variances of the unbiased estimator of T(0)= 0?.Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Calculate the mean(x) mean (y) variance (x) variance(y)