Question

Review: Central Limit Theorem 1 point possible (graded) The Central Limit Theorem states that if X1,…,Xn...

Review: Central Limit Theorem

1 point possible (graded)

The Central Limit Theorem states that if X1,…,Xn are i.i.d. and

E[X1]=μ<∞ ; Var(X1)=σ2<∞,

then

n−−√[(1n∑i=1nXi)−μ]−→−−n→∞(d)Wwhere W∼N(0,?).

What is Var(W)? (Express your answer in terms of n, μ and σ).

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
What is wrong with the following statement of the central limit theorem? Central Limit Theorem.  If the...
What is wrong with the following statement of the central limit theorem? Central Limit Theorem.  If the random variables X1, X2, X3, …, Xn are a random sample of size n from any distribution with finite mean μ and variance σ2, then the distribution of will be approximately normal, with a standard deviation of σ / √n.
Which one of the following statements is true? A. The Central Limit Theorem states that the...
Which one of the following statements is true? A. The Central Limit Theorem states that the sampling distribution of the sample mean, y , is approximately Normal for large n only if the distribution of the population is normal. B. The Central Limit Theorem states that the sampling distribution of the sample mean, y , is approximately Normal for small n only if the distribution of the population is normal. C. The Central Limit Theorem states that the sampling distribution...
Review: Manipulating Multivariate Gaussians 1 point possible (graded) Recall that a multivariate Gaussian N(μ⃗ ,Σ) is...
Review: Manipulating Multivariate Gaussians 1 point possible (graded) Recall that a multivariate Gaussian N(μ⃗ ,Σ) is a random vector Z=[Z(1),…,Z(n)]T where Z(1),…,Z(n) are jointly Gaussian , meaning that the density of Z is given by the joint pdf f:Rn → R Z ↦ 1(2π)n/2det(Σ)−−−−−−√exp(−12(Z−μ⃗ )TΣ−1(Z−μ⃗ )) where μ⃗ i =E[Z(i)],(vector mean). Σij =Cov(Z(i),Z(j))(positive definite covariance matrix). Suppose that Z∼N(0,Σ). Let M denote an n×n matrix. What is the distribution of MZ?
Confidence interval Concept Check 1 point possible (graded) As in the previous section, let X1,…,Xn∼iidexp(λ). Let...
Confidence interval Concept Check 1 point possible (graded) As in the previous section, let X1,…,Xn∼iidexp(λ). Let λˆn:=n∑ni=1Xi denote an estimator for λ. We know by now that λˆn is a consistent and asymptotically normal estimator for λ. Recall qα/2 denote the 1−α/2 quantile of a standard Gaussian. By the Delta method: λ∈[λˆn−qα/2λn−−√,λˆn+qα/2λn−−√]=:I with probability 1−α. However, I is still not a confidence interval for λ. Why is this the case?
Method of Moments Concept Question II 1 point possible (graded) Let (E,{Pθ}θ∈Θ) denote a statistical model...
Method of Moments Concept Question II 1 point possible (graded) Let (E,{Pθ}θ∈Θ) denote a statistical model associated to a statistical experiment X1,…,Xn∼iidPθ∗ where θ∗∈Θ is the true parameter. Assume that Θ⊂Rd for some d≥1. Let mk(θ):=E[Xk] where X∼Pθ. mk(θ) is referred to as the k-th moment of Pθ . Also define the moments map: ψ:Θ →Rd θ ↦(m1(θ),m2(θ),…,md(θ)). What conditions on ψ do we have to assume so that the method of moments produces a consistent and asymptotically normal estimator?...
X1, … Xn are i.i.d. random variables, and E(Xi ) = 3β, Var(Xi ) = 3β^2...
X1, … Xn are i.i.d. random variables, and E(Xi ) = 3β, Var(Xi ) = 3β^2 , i = 1 … n, β > 0. Two estimators of β are defined as β̂ 1 = (X̅ /3) β̂ 2 = (n /3n+1 ) X̅ Show that MSE(β̂ 2) < MSE(β̂ 1) for a sample size of n = 3.
The Central Limit Theorem is used when dealing with: mean from a sample, individual data point...
The Central Limit Theorem is used when dealing with: mean from a sample, individual data point ,chi-squared distributions, or sampling distribution of a standard deviation? When using the CLT, we use σ √ n for the: standard deviation for individual values, mean for the sample, standard deviation of the sample means, or sample size?
1. The Central Limit Theorem A. States that the OLS estimator is BLUE B. states that...
1. The Central Limit Theorem A. States that the OLS estimator is BLUE B. states that the mean of the sampling distribution of the mean is equal to the population mean C. none of these D. states that the mean of the sampling distribution of the mean is equal to the population standard deviation divided by the square root of the sample size 2. Consider the regression equation Ci= β0+β1 Yi+ ui where C is consumption and Y is disposable...
(Central Limit Theorem) An insurance company serves 10 large customers. The insurance claim placed by each...
(Central Limit Theorem) An insurance company serves 10 large customers. The insurance claim placed by each customer in a year is uniformly distributed between 0 and 100. Assume that the insurance claims from different customers are independent. Use the central limit theorem to approximately compute the probability that the total insurance claim placed by all customers in a year exceeds 625. Let Φ(x) denote the cumulative distribution function of a standard normal distribution, i.e. a normal distribution with mean 0...
(05.02 LC) The Central Limit Theorem says that when sample size n is taken from any...
(05.02 LC) The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are true? (4 points) I. The distribution of the sample mean is exactly Normal. II. The distribution of the sample mean is approximately Normal. III. The standard deviation is equal to that of the population. IV. The distribution of the population is exactly Normal. a I and...