WEEK 4 STAT 200 PARTICIPATION TOPIC

 Week 4 Discussion Topic: Expected Value ???

This is a case that you are put in a quandary: to take the cash or not to take the cash. Definitely, you do not want to see the cold cash of $400 offer to you …....

On the other hand, what would be an objective analysis that can guide us to a logical and non-emotional decision to be taken for week 4 discussion?

The answer lies in the expected value (mathematical expectation). There are an abundance of fancy mathematical definition of this statistical term. In the nutshell, it boils down to asking ourselves what the average odds, repeated over and over, per sæcula sæculorum, of winning/gaining is, but with a catch. In this case, we are attaching a value, or even cash value, to the odds. Naturally, the outcome is a cash value of what we should expect from the outcome.

In this particular situation, we would like to ask what would the "average" cash value of each game show will be if that particular game show has been running for years already. In other words, if I go into that game show, how much, on the average. Would I expect to win in this one single game? Here comes the expected value written in table:x

P (x)

x . P (x)

$4000

1/16

$250

$1500

1/16

$93.75

$1000

2/16

$125

-$50

12/16

-$37.50

Expected Value = $431.25