{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment4

# Assignment4 - Statistics 371 Spring 2010 Assignment 4 Due...

This preview shows pages 1–2. Sign up to view the full content.

Statistics 371 Spring 2010 Assignment 4 Due: Thursday July 8 1. We can think of simulations, (often called Monte Carlo Methods) as applications of SRS. These methods are often used to evaluate an integral in high dimensions when the integrand is expensive to compute. The integral correspond to expected values of quantities of interest in the simulation. Here is a toy example estimating a definite integral. Suppose we want to evaluate Af t d t t dt == z z () exp( . ) 0 1 2 0 1 05 2 π . This is the probability that a standard gaussian random variable falls in the interval (, so we know that A=0.3413 . Consider the very large frame Uu ) 01 u N = ( ,. ..., ) 1 that is the finite set of possible values returned by a uniform random number generator and let ) y f u i = ( ) i . Then the population average y N i U is very close to the integral. Any difference is frame error. a) Use the code u<-runif(100,0,1) to generate a simple random sample of 100 units from the frame. Calculate f<-exp(-.5*u*u)/sqrt(2*pi). Hence find an estimate of A and the corresponding 95% confidence interval.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Assignment4 - Statistics 371 Spring 2010 Assignment 4 Due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online