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Get Full Access to UD - ELE 310 - Class Notes - Week 7
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UD / ELEG / ELE 310 / How do we solve for characteristic functions?

# How do we solve for characteristic functions? Description

##### Description: Lectures 10 and 11
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ELEG 310

Lectures 11 and 12

Given mean E[A]=m, variance VAR[A]= We also discuss several other topics like etoro sexuality

Y̲̅ If you want to learn more check out How much blood passes through the glomeruli every minute?  this has no distribution, so its treated as a constant, If you want to learn more check out What are some signs of depression?

Only a changes;                                since time is not random

It is random

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So  [Y̲̅]=  using properties

VAR[Y̲̅] = using theorems directly

New Topic: Characteristic Functions

The characteristic function of a random variable is given by 1st interpretation: expected value of a function of ,

where w is unspecified 2nd interpretation: the fourier transform of the Inverse Fourier transform will be used: Every pdf and its characteristic function form a unique Fourier transform pair.

Example 1: Exponential Random Variable     Example 2: Uniform Variable - suppose is a uniform variable   Both Examples 1 and 2 are continuous-time examples.

If discrete random variable takes on integer values only ↓    integer value                                        density                delta function Locations where discrete

random variable have values

Characteristic Function:   Example 3: Bernoulli Random Variable, a.k.a “easiest possible case”

Fair coin      Example 4: Using Characteristic Function    Derivative    using formula     = ✔

constant      ✔

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