- Convergence in mean square, If a sequence of r.v. X₁, converges to X in mean square, with E[X²] <∞, show that a) E[X] → E[X] as n →∞0. E[X2] → E[X²] as n → ∞. b) c) Cov(X, X)→Var[X], as n → ∞ where notations Cor and Var stand for covariance and variance.
- Convergence in mean square, If a sequence of r.v. X₁, converges to X in mean square, with E[X²] <∞, show that a) E[X] → E[X] as n →∞0. E[X2] → E[X²] as n → ∞. b) c) Cov(X, X)→Var[X], as n → ∞ where notations Cor and Var stand for covariance and variance.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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now, i have removed honor code violation, please solve it
![4. Convergence in mean square,.
If a sequence of r.v. X₁, converges to X in mean square, with E[X2] < oo, show that
E[X] →→ E[X] as n →∞0.
E[X] →→ E[X²] as n → ∞.
c)
Cov(X₁, X)→ Var[X], as n → ∞
where notations Cou and Var stand for covariance and variance.
a)
b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F550e334d-17b6-4ad8-833c-886e1564fdb0%2F68b1f90d-e8dc-4182-979f-bdf24e083ff9%2Fx40xfya_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Convergence in mean square,.
If a sequence of r.v. X₁, converges to X in mean square, with E[X2] < oo, show that
E[X] →→ E[X] as n →∞0.
E[X] →→ E[X²] as n → ∞.
c)
Cov(X₁, X)→ Var[X], as n → ∞
where notations Cou and Var stand for covariance and variance.
a)
b)
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