Homework Help is Here – Start Your Trial Now!
Math
Probability
To simplify the calculations, we make use of the following random variables for the empirical distribution P: for i = {1, 2,...,n}, with Pn(i) = 1/n. (i) Verify that Ŷ = a + BX + ê. Using this, show that Conclude that X (i) = x₁, Ŷ (i) = Yi, ê(i) = Ei, (ii) Show that Vy := Varp (Ý) = = 3²¹vx + Varp (ê) + 2/6 Cov, (X, ê). Evy = ß²v₂ + E Var (ê) + 2ß E Covp₁ (‚ ê). n - 1 n Pn (Hint: recall that if v = Var (X) is the variance of the empirical distribution for i.i.d sample outcomes x1, x2,., n of a random variable X, then we know Ev(X₁, X2,..., Xn) n-1 Var X.4) E Var (2) = ·0²

To simplify the calculations, we make use of the following random variables for the empirical distribution P: for i = {1, 2,...,n}, with Pn(i) = 1/n. (i) Verify that Ŷ = a + BX + ê. Using this, show that Conclude that X (i) = x₁, Ŷ (i) = Yi, ê(i) = Ei, (ii) Show that Vy := Varp (Ý) = = 3²¹vx + Varp (ê) + 2/6 Cov, (X, ê). Evy = ß²v₂ + E Var (ê) + 2ß E Covp₁ (‚ ê). n - 1 n Pn (Hint: recall that if v = Var (X) is the variance of the empirical distribution for i.i.d sample outcomes x1, x2,., n of a random variable X, then we know Ev(X₁, X2,..., Xn) n-1 Var X.4) E Var (2) = ·0²

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
See similar textbooks
icon
Related questions
Question

Can you show me the answer to (i) and (ii)? Thank you so much for your help

In this exercise, we fill in a key missing step in our computation of Eô² = "=²0². Namely, we will show that n Conclude that E vy (1) n To simplify the calculations, we make use of the following random variables for the empirical distribution Pn: (ii) Show that n 1 = for i = {1, 2,...,n}, with Pn(i) = 1/n. (i) Verify that Ŷ = a + ß + ĉ. Using this, show that = Â(i) = xi, Ŷ (i) = Yi, ê(i) = ɛi, -0² + B²vx. Vy := Varp (Ý) 3²v₂ + Varp (ê) + 2/3 Cov, (Â, ê). Evy = 3²v + E Var (2) + 2/3 E Covin E Var în (â) = η - 1 - -0². (Â,Ê). n (Hint: recall that if v = Var (X) is the variance of the empirical distribution for n i.i.d sample outcomes 1, 2,...,n of a random variable X, then we know Ev(X₁, X2, ..., Xn) = n-1 Var X.4) n
Transcribed Image Text:In this exercise, we fill in a key missing step in our computation of Eô² = "=²0². Namely, we will show that n Conclude that E vy (1) n To simplify the calculations, we make use of the following random variables for the empirical distribution Pn: (ii) Show that n 1 = for i = {1, 2,...,n}, with Pn(i) = 1/n. (i) Verify that Ŷ = a + ß + ĉ. Using this, show that = Â(i) = xi, Ŷ (i) = Yi, ê(i) = ɛi, -0² + B²vx. Vy := Varp (Ý) 3²v₂ + Varp (ê) + 2/3 Cov, (Â, ê). Evy = 3²v + E Var (2) + 2/3 E Covin E Var în (â) = η - 1 - -0². (Â,Ê). n (Hint: recall that if v = Var (X) is the variance of the empirical distribution for n i.i.d sample outcomes 1, 2,...,n of a random variable X, then we know Ev(X₁, X2, ..., Xn) = n-1 Var X.4) n
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS