Homework #9

All problems MUST be in a SINGLE *.m file and be in separate blocks using '%% Problem X'. Otherwise you will not receive credit. You may need additional files for class definitions or functions. See class webpage for naming convention.

Contents

Problem 1

In class we used random numbers to find the area of a circle. Use the same type of method to estimate the result of:

$\int_0^{\pi/2} \cos{x} \mathrm{d}x$

Problem 2

A search for a new particle is underway at a particle accelerator. The particle decays with a characteristic signal that can be identified with 100% confidence. The theory predicts that under experimental conditions, the particle will be created at a rate of 1 per day. The experiment is only allotted four days of beam time. If the particle does exist and the theory is correct, what is the probablity no events are observed? Find the answer by simulating this experiment 1000 times.

Problem 3

The exponential function can be defined as

$e^x = \lim_{n\to \infty}{ (1+\frac{x}{n})^n}$

for x=1, show the deviation of this expression from exp(x) as a function of n. Use a log-log plot.

Problem 4

Use 'poissrnd' to reproduce the top-right figure showing the probability mass function:

http://en.wikipedia.org/wiki/Poisson_distribution


Published with MATLAB® R2014b