×
Get Full Access to UD - ELE 310 - Class Notes - Week 7
Get Full Access to UD - ELE 310 - Class Notes - Week 7

×

UD / ELEG / ELE 310 / How do we solve for characteristic functions?

# How do we solve for characteristic functions? Description

##### Description: Lectures 10 and 11
8 Pages 186 Views 3 Unlocks
Reviews

ELEG 310

Lectures 11 and 12

Given mean E[A]=m, variance VAR[A]=

We also discuss several other topics like etoro sexuality

Y̲̅If 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

We also discuss several other topics like clifford intro

If you want to learn more check out What is the iceberg of stuttering?
We also discuss several other topics like What is the period between early childhood and early adolescence?

↘given

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

✔

Page Expired
It looks like your free minutes have expired! Lucky for you we have all the content you need, just sign up here
References: