Question

1. Suppose a parameter family has parameter q = E (X^3), where q is real. Devise...

1. Suppose a parameter family has parameter q = E (X^3), where q is real. Devise an estimator of q (hint: use the “Golden Rule”) and show it is unbiased and consistent for q.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose a parameter family has parameter q = E(X3), where is q is real. Devise an...
Suppose a parameter family has parameter q = E(X3), where is q is real. Devise an estimator of q (hint: use the “Golden Rule” estimation) and show it is unbiased and consistent for q.
If P(X=x) = lambda ^x, e^(-lambda)/x! Poisson distrubtion random variable X has lambda = 3 L=...
If P(X=x) = lambda ^x, e^(-lambda)/x! Poisson distrubtion random variable X has lambda = 3 L= Sum (i=1 to n) Xi/n Is L an unbiased estimator of lambda? Is L consistent estimator of lambda?
A program devise a recursive algorithm to find a2n, where a is a real number and...
A program devise a recursive algorithm to find a2n, where a is a real number and n is a positive integer (hint: use the equality a2n+1 = (a^2n)^2
1. Remember that a Poisson Distribution has a density function of f(x) = [e^(−k)k^x]/x! . It...
1. Remember that a Poisson Distribution has a density function of f(x) = [e^(−k)k^x]/x! . It has a mean and variance both equal to k. (a) Use the method of moments to find an estimator for k. (b) Use the maximum likelihood method to find an estimator for k. (c) Show that the estimator you got from the first part is an unbiased estimator for k. (d) (5 points) Find an expression for the variance of the estimator you have...
Suppose X and Y are independent variables with E(X) = E(Y ) = θ, Var(X) =...
Suppose X and Y are independent variables with E(X) = E(Y ) = θ, Var(X) = 2 and Var(Y ) = 4. The two estimators for θ, W1 = 1/2 X + 1/2 Y and W2 = 3/4 X + 1/4 Y . (1) Are W1 and W2 unbiased? (2) Which estimator is more efficient (smaller variance)?
Let p and q be two real numbers with p > 0. Show that the equation...
Let p and q be two real numbers with p > 0. Show that the equation x^3 + px +q= 0 has exactly one real solution. (Hint: Show that f'(x) is not 0 for any real x and then use Rolle's theorem to prove the statement by contradiction)
Let X1, X2, . . . , Xn be iid following exponential distribution with parameter λ...
Let X1, X2, . . . , Xn be iid following exponential distribution with parameter λ whose pdf is f(x|λ) = λ^(−1) exp(− x/λ), x > 0, λ > 0. (a) With X(1) = min{X1, . . . , Xn}, find an unbiased estimator of λ, denoted it by λ(hat). (b) Use Lehmann-Shceffee to show that ∑ Xi/n is the UMVUE of λ. (c) By the definition of completeness of ∑ Xi or other tool(s), show that E(λ(hat) |  ∑ Xi)...
Suppose the random variable X has Poisson distribution with rate parameter l. Let g be the...
Suppose the random variable X has Poisson distribution with rate parameter l. Let g be the function defined by g(u) = 1/(u+1) , u >0. Show E(g(X)) >g(E(X)).
If X and Y are independent, where X is a geometric random variable with parameter 3/4...
If X and Y are independent, where X is a geometric random variable with parameter 3/4 and Y is a standard normal random variable. Compute E(e X), E(e Y ) and E(e X+Y ).
If X and Y are independent, where X is a geometric random variable with parameter 3/4...
If X and Y are independent, where X is a geometric random variable with parameter 3/4 and Y is a standard normal random variable. Compute E(e^X), E(e^Y ) and E(e^(X+Y) ).