My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Thanks Tree1Thanks
Reply
 
LinkBack Thread Tools Display Modes
October 23rd, 2017, 07:18 PM   #11
Senior Member
 
Joined: Aug 2012

Posts: 1,638
Thanks: 415

Quote:
Originally Posted by romsek View Post
Ok, I've got it. Tricky little devil but really not that bad.
Now it's perfectly clear. Thanks. They're looking at a ternary input string with probabilities as given, and they're asking about the asymptotic behavior of the output string.

The voltages and even the input string itself are not relevant. We're building a bitstring by appending 0, 10, or 11 with the given probabilities. Or we can think of the input as being a ternary string.

I'm thinking about it like this. With probability .4 we append one bit; and with probability .6 we append two. So the expected number of output bits for an input string of length n is .4(1) + .6(2) = 1.6n. This seems reasonable to me but I can see I'm hiding the limit computation. There's no reason that an input string of length n must generate an output stream of exactly 1.6n. It's only true statistically.

Likewise we add a single 1 with probability .3, and two 1's with probability .3. So the expected number of 1's is .3(1) + .3(2) = .9n.

Now .9n/1.6n = .5625 as required. But there is something a little fishy with my thinking. I made the limits disappear and I'm not exactly sure what allows me to do that. Can anyone who knows probability theory clarify my confusion?

ps -- The probability that an output bit is 0 is just 1 minus .5625, you don't need to do the second computation.

Last edited by Maschke; October 23rd, 2017 at 07:26 PM.
Maschke is offline  
 
October 23rd, 2017, 08:46 PM   #12
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,604
Thanks: 817

Quote:
Originally Posted by Maschke View Post
It's only true statistically.
yes
romsek is offline  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
binary, bit, messages, pdf, probability



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Binary Probability Formula Karma Probability and Statistics 9 July 17th, 2017 02:28 PM
Teachers Day Messages Saginogdu7422 Art 0 September 4th, 2016 04:02 AM
Why do I get these Error Messages? vagulus Elementary Math 4 February 16th, 2015 05:34 AM





Copyright © 2017 My Math Forum. All rights reserved.