Transcript box-muller

Exercise using Excel (see intro to
Excel at end)
1.
Using Excel’s rand() function, generate a column of 100 random
numbers in the range -1 to +1. Plot a histogram (see histogram slide)
of these numbers. Note that they are uniformly distributed.
2.
Also using Excel, generate a column of 100 normally distributed
random numbers with mean=0.0 and standard deviation=1.0. (Hint:
Use the polar form.) Also, plot (histogram) these random numbers.
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Do not use Excel’s built in normdist(), normsdist(), normsinv(), or an other
Excel built in norm*() function. They aren’t generally available in game
engines.
3.
Also using Excel, generate a column of 100 normally distributed
random numbers with mean=0.5 and standard deviation=0.25. (Hint:
Use the polar form.) Also, plot (histogram) these random numbers.
4.
Create one plot (histogram) with all sets of random numbers.
5.
Answer the following. What happens when U1=0?
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Creating and plotting a
histogram using Excel
Steps:
1. Create column of data.
2. Create column of bins
(categories).
3. Select “array” of
columns for histogram.
4. Type in =frequency(
a2:a1001, e2:e23 ) and
then type ctrl+shift+Enter.
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Histogram result
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Exercise using Unity and C#
Create a new class called MyRandomGenerator, and
implement the following:
6. Write a function called uniform that, given a min and
max, generates a random number in the interval
[min,max].
7. Write a function called normalPolar that, given a mean
and standard deviation, generates a random number
sampled from that distribution.
8. Write a function called normalCartesian that, given a
mean and standard deviation, generates a random
number sampled from that distribution.
9. Using some built in function to get the time, determine
how much time is required to generate 1000 random
numbers via each of the above methods. (If 1000
random numbers can be generated in < 5 seconds, use
a number larger than 1000.)
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Exercise using Java, C/C++, or C#
10. Real numbers (float and double) and integers (int,
short, char, byte (in Java)) are represented using a finite
number of bits. Therefore, we can only have a finite
number of real numbers or integers. What is the
smallest non-zero number that can be represented by a
double? (Hint: Consult java.lang.Double or limits.h.)
11. Given the above, is there a maximal value for Z0 in the
equation below?
12. Is the range of possible values sampled from a uniform
distribution bounded or unbounded? Is the range of
possible values sampled from a normal distribution
bounded or unbounded? Is the range of values
generated by an implementation of the polar form of the
Box-Muller algorithm bounded or unbounded?
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A VERY BRIEF INTRODUCTION
TO EXCEL
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Values and calculations
 Constants in col A; expressions in col B (calling built in
functions and referring to values in other cells..
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 Copy exp in B1, select multiple cells, and paste. Note
cell changes automatically.
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 Use : to refer to multiple cells. For example,
=sum(a1:a4) calculates the sum of the values in cells a1
through a4.
 Avoid automatic cell changes by using $.
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