Let Xi ∼iid Ber(p). Define Y = Xbar. Approximate the mean of W = g(Y )...

Let Xi ∼iid Ber(p). Define Y = Xbar. Approximate the mean of W = g(Y ) = Y (1 − Y ) using the first and second order delta methods. Also, estimate the variance of W using the first order method.

Solutions

Expert Solution

we will use delta method of first order which is univariate method as well. i am sharing the image containing the solution of the questing. i am using the method of central limit theorem also .

the first order delta method is ,

x₁, x₂....x_n is sequence of random variables,

if for n tends to infinite,

sqrt(n)[x_n-p]--d--->N(0,sigma²)

where, p = mean of x_1,x₂, ....... ,x_n

and singma² = variance of x₁,x₂, ...., x_n

then for n tends to infinite,

sqrt(n)[g(x_n)-g(p)]--d--->N(0,sigma².[g^' (p)]²)

where g^'(p) exist and non zero.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Let p, q, g : R → R be continuous functions. Let L[y] := y'' +...

Let p, q, g : R → R be continuous functions. Let L[y] := y'' + py' + qy. (i) Explain what it means for a pair of functions y1 and y2 to be a fundamental solution set for the equation L[y] = 0. (ii) State a theorem detailing the general solution of the differential equation L[y] = g(t) in terms of solutions to this, and a related, equation.

Let Xi = lunch condition on day i (rice/noodles) P(Xi+1 = rice| Xi-1 = rice, Xi...

Let Xi = lunch condition on day i (rice/noodles) P(Xi+1 = rice| Xi-1 = rice, Xi = rice) = 0.7 P(Xi+1 = rice| Xi-1 = noodles, Xi = rice) = 0.6 P(Xi+1 = rice| Xi-1 = rice, Xi = noodles) = 0.3 P(Xi+1 = rice| Xi-1 = noodles, Xi = noodles) = 0.55 Q1. Is {Xn} a Markov Chains? Why? Q2. How to transform the process into a M.C. ?

Example 3.5: Again let X = Y = R. Define g by g(x) = x2. The...

Example 3.5: Again let X = Y = R. Define g by g(x) = x2. The graph of this function has the familiar parabolic shape as in Figure 3.1(b). Then for example, g([0, 1]) = [0, 1], g([1, 2]) = [1, 4], g({−1, 1}) = {1}, g−1([0, 1]) = [−1, 1], g−1([1, 2]) = [− √ 2, −1]∪[1, √ 2], g−1([0, ∞)) = R. *I need help understanding why each example in bold is the answer it is* *Please explain...

Let G and H be groups. Define the direct product G X H = {(x,y) |...

Let G and H be groups. Define the direct product G X H = {(x,y) | x ∈ G and y ∈H } Prove that G X H itself is a group.

Let G be a group, and let a ∈ G be a fixed element. Define a...

Let G be a group, and let a ∈ G be a fixed element. Define a function Φ : G → G by Φ(x) = ax−1a−1. Prove that Φ is an isomorphism is and only if the group G is abelian.

Let Xi be a random variable that takes on the value 1 with probability p and...

Let Xi be a random variable that takes on the value 1 with probability p and the value 0 with probability q = 1 − p. As we have learnt, this type of random variable is referred to as a Bernoulli trial. This is a special case of a Binomial random variable with n = 1. a. Show the expected value that E(Xi)=p, and Var(Xi)=pq b. One of the most common laboratory tests performed on any routine medical examination is...

Question