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Lecture 11: Probability and Random Numbers in MATLAB, Study notes of Computer Science

Cornell University Computer Science

A part of lecture notes from a university course on matlab and numerical computing. It covers the topics of probability and random numbers, including uniform probability distribution, pseudorandom numbers, and generating random integers using matlab's rand and round functions. The document also includes examples and exercises.

Typology: Study notes

Pre 2010

Uploaded on 08/31/2009

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Previous Lecture:

User-defined functions

Examples with varying numbers of input and output parameters

Local memory space

Today’s Lecture:

Probability and random numbers

1-d array—vector

More MATLAB graphics

Announcement:

Prelim 1 will be returned at end of lecture. If your paper

isn’t here, pick it up from CS1112 consultants in ACCEL

during consulting hrs (today after 4pm)

Read from Insight

Discover Study notes of Computer Science Cornell University

Partial preview of the text

Download Lecture 11: Probability and Random Numbers in MATLAB and more Study notes Computer Science in PDF only on Docsity!

^ Previous Lecture:^

User-defined functions^ ^

Examples with varying numbers of input and output parameters Local memory space

^ Today’s Lecture:^

Probability and random numbers 1-d array—vector More MATLAB graphics

^ Announcement:^

Prelim 1 will be returned at end of lecture. If your paperisn’t here, pick it up from CS1112 consultants in ACCELduring consulting hrs (today after 4pm) Read from

Insight

February 24, 2009

Lecture 11

Random numbers ^ Pseudorandom

numbers in programming

^ Function

rand(…)

generates random real

numbers in the interval (0,1). All numbers in theinterval (0,1) are equally likely to occur—uniformprobability distribution. Examples:

rand(1)

one random # in (0,1)

6*rand(1)

one random # in (0,6)

6*rand(1)+

one random # in (1,7)

February 24, 2009

Lecture 11

Sanity check: rand and randn >>^

n=^

>>^

x=^

rand(n,1);

>>^

ave=

sum(x)/n

ave

>>^

y=^

randn(n,1);

>>^

ave=

sum(y)/n

ave

>>^

stdDev=

std(y)

stdDev

February 24, 2009

Lecture 11

Random noise ^ Plot y=sin(x) across [0,

π] and add random noise

if Say, noise is .1*randn if x is in above range Two versions: vectorized vs. non-vectorized

π^

≤^ x

February 24, 2009

Lecture 11

1-d array:

vector

^ An array is a named collection of like dataorganized into rows or columns ^ A 1-d array is a row or a column, called a

vector

^ An

index

identifies the position of a value in a

vector

score

February 24, 2009

Lecture 11

Array index starts at 1

Let k be the index of vector x, then ^ k must be a positive integer ^ 1<= k <= length(x) ^ To access the k

th^ element: x(k)

-4^ -

1 2

4 5

February 24, 2009

Lecture 11

(rand(1)6)*

February 24, 2009

Lecture 11

round(rand(1)6)*

February 24, 2009

Lecture 11

round(rand(1)6)*

(rand(1)6)*

February 24, 2009

Lecture 11

round(rand(1)6)*

ceil(rand(1)6)* 2

February 24, 2009

Lecture 11

Possible outcomes from rolling a fair 6-sided die^1

February 24, 2009

Lecture 11

Simulation^1

February 24, 2009

Lecture 11

Simulation^1

February 24, 2009

Lecture 11 3

Lecture 11: Probability and Random Numbers in MATLAB, Study notes of Computer Science

Related documents

Partial preview of the text

Download Lecture 11: Probability and Random Numbers in MATLAB and more Study notes Computer Science in PDF only on Docsity!

^ Previous Lecture:^ 

^ Today’s Lecture:^ 

^ Announcement:^ 

Random numbers ^ Pseudorandom

numbers in programming

^ Function

rand(…)

generates random real

numbers in the interval (0,1). All numbers in theinterval (0,1) are equally likely to occur—uniformprobability distribution.  Examples:

rand(1)

one random # in (0,1)

6*rand(1)

one random # in (0,6)

6*rand(1)+

one random # in (1,7)

Sanity check: rand and randn >>^

n=^

>>^

x=^

rand(n,1);

>>^

ave=

sum(x)/n

ave

>>^

y=^

randn(n,1);

>>^

ave=

sum(y)/n

ave

>>^

stdDev=

std(y)

stdDev

Random noise ^ Plot y=sin(x) across [0,

π] and add random noise

if  Say, noise is .1*randn if x is in above range  Two versions: vectorized vs. non-vectorized

π^

≤^ x

1-d array:

vector

^ An array is a named collection of like dataorganized into rows or columns ^ A 1-d array is a row or a column, called a

vector

^ An

index

identifies the position of a value in a

vector

Array index starts at 1

Let k be the index of vector x, then ^ k must be a positive integer ^ 1<= k <= length(x) ^ To access the k

th^ element: x(k)

Possible outcomes from rolling a fair 6-sided die^1

Simulation^1

Simulation^1

Simulation^1

^ Previous Lecture:^

^ Today’s Lecture:^

^ Announcement:^

Random numbers ^ Pseudorandom

^ Function

numbers in the interval (0,1). All numbers in theinterval (0,1) are equally likely to occur—uniformprobability distribution. Examples:

Random noise ^ Plot y=sin(x) across [0,

if Say, noise is .1*randn if x is in above range Two versions: vectorized vs. non-vectorized

^ An array is a named collection of like dataorganized into rows or columns ^ A 1-d array is a row or a column, called a

^ An

Let k be the index of vector x, then ^ k must be a positive integer ^ 1<= k <= length(x) ^ To access the k