pattern recognition lab 2 ta : nouf al-harbi::
DESCRIPTION
Theoretical Concept Part 1 3TRANSCRIPT
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Lab objective: Illustrate the uniform distribution of a
random variable using Matlab
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Theoretical Concept
Part 1
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Suppose a die is rolled. What is the probability that the die will land on 5 ?
On 4 , on 2?.…
Dice Experiment
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Dice Experiment When a die is rolled there are 6 possible outcomes represented by: X = { 1, 2, 3, 4, 5, 6 }. Each outcome is equally likely to occur
If a die is rolled 1200 times Then , each of outcome should occur
1200/6 = 200 times
FrequencyF(X)
Outcome x
200 1200 2200 3200 4200 5200 6
Frequency distribution
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Dice Experiment What’s the probability for occurring each
outcome ..? P(X = 6) = 200/1200 =1/6 P(X=3)=P(X=1)=200/1200=1/6
A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence
If each outcome has the same probability then probability density function is called
“uniform distribution”
Probability P(X=x) Outcome x
1/6 11/6 21/6 31/6 41/6 51/6 6
probability distribution
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What’s uniform distribution?..
We obtain a uniform density function when the outcomes of an experiment (random process) are equally likely to occur.
1 2 3 4 5 6
1outcome
Prob. Of occurrence
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Practical Applying
Part 2
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Applying dice experiment by Matlab
1. Generate N random values uniformly distributed in the closed range [1,6].
2. Find the frequency distribution of each outcome (1-6)
(i.e. how many times each outcome occur?)
3. Find the probability density function p(x)
4. Plot p
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Generate N random values uniformly distributed in the closed range [1,6].
Step 1
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rand functionrand(1,N)
Generates N random values uniformly distributed in the open range ]0,1[.
Write the following in Matlab & see the result: r = rand(1,20) generates 1-D array of one row and 20 columns Random values range between 0 and 1
To change the period we can use fix function
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fix function x = fix( 6 * r ) + 1; Writing the previous line converts r
into random values in the closed period [1,6]
For Dice Experiment, What are the values of vector x represent..?
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Find the frequency distribution of each outcome (1-6)
Step 2
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Find the frequency distribution of outcome we’ll make a counter for each outcome
1 2 3 4 5 6120 191 199 210 300 180f
Event no. 1 2 3 4 5 6 7 … 1200
outcome 2 1 1 2 5 6 6 … 2
N
x
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Find the probability density function p(x)
Step 3
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Find the probability density function p(x)
We can easily calculate the probability the outcome frequency divided by the no.
of events P=f/N
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Plot the probability density function p(x)
Step 4
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plot p(x) plot function has different forms , depending on
input arguments. If you have two vectors y and x
plot (x,y) produces a graph of y versus x If you have one vector x
plot(x) produces a graph of columns of x versus their index
To change the axis scale, that is x starts from xmin to xmax and y starts from ymin to ymax use the command:
axis([xmin xmax ymin ymax])
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plot p(x) If we have more than one graph, we
can use figure command to create a new figure window It’s useful to avoid draw the new graph
over the previous one For more information about plot
function and its forms type help plot on command window
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20 1. N = 100;2. r = rand(1,N); 3. x = fix( 6 * r ) + 1;4. f = zeros(1,6);5. for i = 1 : N6. if x(i) == 1 f(1) = f(1) + 1;7. elseif x(i) == 2 f(2) = f(2) + 1;8. elseif x(i) == 3 f(3) = f(3) + 1;9. elseif x(i) == 4 f(4) = f(4) + 1;10.elseif x(i) == 5 f(5) = f(5) + 1;11.else f(6) = f(6) + 1;12.end13.end14.F15.plot(f)16.axis([0 7 0 1.5])17.p = f /N18.figure, plot(p)19.axis([0 7 0 0.3])
Full code
Try larger values of N:
(1000,10000 )and notice the graph
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•Write a Matlab function to illustrate a uniform distribution of coin experiment .•A function should take the number of events N as an argument
Exercise 1