Wednesday, March 21, 2007

9-8: Math Expectation

Well, we never really got a lecture on this section, so I'll be presenting just my own example of the lesson...

The mathematical expectation is the weighted average based on the expected probabilities. It is the weighted average for a random experiment each time it is run. It is a value that one calculates based on the outcomes for each event in a random experiment.

The mathematical expectation, or E, of a random experiment is the sum:

E = P(A1) a1 + P(A2) a2 + P(A3) a3 + . . . + P (An) an

for the n mutual exclusive events A1, A2, A3, ..., An in the experiment.

Outcomes = A1, A2, ..., An
Values of corresponding outcomes = a1, a2, ..., an

My Example:

Jane Doe is playing "Let's-Roll-the-Dice-and-See-How-Many-Points-I get" with her brother John Doe. Each roll of a single dice is considered an event. The points are as follows:
- Roll a 6: Win 72 points
- Roll a 4: Win 35 points
- Roll a 2: Win 27 points
- Roll an odd number: Lose 13 points

It is Jane's turn. Drawing a chart makes finding the mathematical expectation easier.
Odd # = 1, 3, 5 = 3/6 probability


>Note: Multiply Points for each with Probability to result in the last column.


>Then add up all the values you get from the Points * P(A) to finally get the mathematical expectation.
15.833 = average (after many many trials) points PER GAME

YAY! That sums it up. (Mr. French, that was my one original example that I made up, since no lecture was given and therefore, no example was shown to us in class.)

Here's a site for moredifferent examples/help on the topic: http://www.tpub.com/math2/86.htm


Soooo as a co-head of publicity for Leo Club, I think it's only appropriate for me to tell everyone that THE 2ND ANNUAL MR. FLINTRIDGE PREP is coming soon! It's on Friday, March 30th in the Norris Auditorium at 5:30. COME EVERYONE! It's going to be FUN and HYSTERICAL. Last year's was a big success, and this year's should be better!

These are the senior guys running for the crown this year:
Matt Adesuyan
Matt Brown
Sean & Mack Carroll (C-Unit)
Alex Jacobs
Ryan Lamont
Daniel Madore
James Mears
Casey Neumeier
Bryan Russell
Drew Titus
Jeff Wagner
Nick Weinstein
James Woolley
... It should and WILL be incredibly amazing SO I EXPECT EVERYONE TO COME!

Michelle you're technically supposed to be up next, but Amira took your spot. So Amira's up next, but she already posted her blog... so umm yeah... Kaori?

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