Xy Xy Xn is a random sample from a normal population ...... 2 x², is an unbiased estimator i = 1 P (u, 1). Show that t = %3D of u² + 1.
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- Find the characteristic function of the geometric distribution given by P(X = r) = q' p, r = 0, 1, 2, ..., ∞, p + q = 1. %3D Hence find the mean and variance.Suppose that Z given Y = y has a normal dlistibution with mean zero and variance y^2 and that Y has a x^2 distribution with v degrees of freedom. find the variance of W = Z/sqrt(Y).Suppose Of Y=3xt 2 and Z= X/4 e^. Find the distribution x~
- The average weight of a Coastal male Grizzly Bear is approximately normal with E(x); =795 pounds and SD * (x) = 80 pounds. 8. How likely is it to randomly select 64 Coastal male Grizzly Bears with a sample average weight of 810 pounds or more? Which density curve is the best model for this problem?5. The equation of the normal line to the curve 3y3 = px² – q_ is 9x +4y = 10 at x = 2. Find p and q. %3DThe first three moments of a distribution about the value 2 of a variable are 1,16 and-40. Show that the mean is 3, the variance is 15 and µ3= -86. Also show that the first three moments about X=0 are 3,24and 76
- Let X₁, ..., X be a random sample from a gamma distribution with a x = 2 and 3 = = 0. '1' 1. Find the simplified likelihood of 0 given x: L(01x). 2. Find the maximum likelihood estimator of 0,0 MLE* is unbiased. 3. Show that the value you found for 0 MLElet 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)WX1,., X,Let it be a random sample chosen from a normal distribution with a mean of m and a variance of 10.P (X, – X)² < 44 = 0.025 what is the value of the sample size n? O A. 13 О В. 14 Ос. 11 O D. 12