Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²
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topic: estimation
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Suppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?Show that: if A occurs in a larger proportion of cases where B is than where it is not, then B will occur in a larger proportion of cases where A is than where A is not.
- Suppose that the continuous two-dimensional random variable (X, Y ) is uniformly distributed over the square whose vertices are (1, 0), (0, 1), (−1, 0), and (0, −1). Find the Correlation Coefficient ρxyare F2 and F3 conservative? also what about parts B and C?Suppose that Z1, Z2, . . . , Zn are statistically independent random variables. Define Y as the sum of squares of these random variables
- Let Mx, y be the moment generating function of random variables that are not independent of X and Y. Which of the following / which are not the properties of the function Mx, y?Define the random process {Xt} by Xt = et + θ et−1. Show this process is weakly stationary.If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?
- FOR THIS, WE REJECT THE NULL FOR BOTH MODELS.You may use homogenous, exact/inexact, linear, Bernoulli, or second order reducible to first orderIf X1, X2, ... , Xn constitute a random sample of size nfrom a geometric population, show that Y = X1 + X2 +···+ Xn is a sufficient estimator of the parameter θ.
