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Welcome back!
Lecture 7 Statistics and The Central Limit
Theorem (today) Lecture 8 Solving Differential
Equations with Fourier Transforms (April
30) Problems/ revision class in w/b May 7. (May
7 is a Bank Holiday).
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REVISION
NB Convolution in this case written as function
of x
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Lecture 7Statistics and the Central Limit
Theorem

• OUTLINE
• - Probability density functions
• Weighing apples
• Relationship between probability density
• and Fourier transforms?
• - Why normal distributions?

• Refs
• The Fourier Transform and its Applications, RN
  Bracewell, (2nd Ed) Ch. 15/ (3rd Ed) Ch. 16.
• Mathematical Methods for Physics and Engineering
  (2nd Ed), Riley, Hobson, and Bence, Ch. 26.

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Lets roll some dice.
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1. Introduction
Probability density functions
Random variable
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Assume uniform distribution
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2. Some numerical experiments
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3. Theory
(a) 2 apples
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Does this make sense?
180
220
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(b) n apples
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Example n10
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4. Central limit theorem
Gaussian Normal
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5. Conclusion and things to think about
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Remarkable fact