Let X be a continuous random variable with probability density function fx, and let g: R → R be a continuous real valued function defined on the real numbers. The Law Large Number (LLN) says E-1 9(X;) → E[g(X)] = L, g(x) fx(x)dx, リ= as n → 0, where {X¡}. are independent identically distributed (iid) samples of X. j=1 (a) Use rand and the LLN to approximate , sin x dx and check your approximation against the true value of the integral as you take n larger and larger. (Hint: If
Let X be a continuous random variable with probability density function fx, and let g: R → R be a continuous real valued function defined on the real numbers. The Law Large Number (LLN) says E-1 9(X;) → E[g(X)] = L, g(x) fx(x)dx, リ= as n → 0, where {X¡}. are independent identically distributed (iid) samples of X. j=1 (a) Use rand and the LLN to approximate , sin x dx and check your approximation against the true value of the integral as you take n larger and larger. (Hint: If
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Let X be a continuous random variable with probability density function fx, and let
g: R → R be a continuous real valued function defined on the real numbers. The Law o
Large Number (LLN) says
E-19(X;) → E[g(X)] = , g(x) fx(x)dx,
%3D
j=1
as n → 00, where {Xj};=1
are independent identically distributed (iid) samples of X.
(a) Use rand and the LLN to approximate sin x dx and check your approximation
against the true value of the integral as you take n larger and larger. (Hint: If
X~U(0,1), then fx (x) = 1, if 0 < x< 1, and fx (x) = 0 for all other values of x.
(b) Now repeat Part (a), but instead approximate Icos Tx|2.5 e-10x dx and observe
convergence as you take n larger and larger.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fb529d9-2cab-4111-a022-18fbe95ed8ac%2F734776cb-2843-46c0-9a1a-75fce078c77f%2Ft42d4fs_processed.png&w=3840&q=75)
Transcribed Image Text:Let X be a continuous random variable with probability density function fx, and let
g: R → R be a continuous real valued function defined on the real numbers. The Law o
Large Number (LLN) says
E-19(X;) → E[g(X)] = , g(x) fx(x)dx,
%3D
j=1
as n → 00, where {Xj};=1
are independent identically distributed (iid) samples of X.
(a) Use rand and the LLN to approximate sin x dx and check your approximation
against the true value of the integral as you take n larger and larger. (Hint: If
X~U(0,1), then fx (x) = 1, if 0 < x< 1, and fx (x) = 0 for all other values of x.
(b) Now repeat Part (a), but instead approximate Icos Tx|2.5 e-10x dx and observe
convergence as you take n larger and larger.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
