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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
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.
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