[cross-posted to sci.stat.edu,sci.stat.math,k12.ed.math]
I'm teaching a GE stat course, my first time teaching stat, and am
having some points of confusion. Here is one of my questions:
Suppose I have a probability distribution as follows:
Sample space:
1.5, 2.0, 2.5, 3.5, 4.0, 4.5
and each of these outcomes is equally likely. So, if my random variable
is x, then
P(x=1.5) = 1/6
P(x=2) = 1/6
and so on...
To draw a probability distribution histogram, I wanted to make the bar
for each outcome have a height of 1/6, but I became confused over this
point:
for x=2.0, the bar can only be on half unit wide, because of the
neighboring outcomes 1.5 and 2.5
(until I had encountered this particular problem, I had always made the
bars for each outcome a width of one unit wide, with a height equal to
P(x=that outcome) and with the outcome value centered horizontally on
the bar).
But it seems to me, each of the bars should have an equal width.
But if there are six bars (because of six outcomes) and each is only
half a unit wide, and 1/6 of a unit tall, then the total area under the
distribution is only 1/2 and not 1. This bothered me.
But the solution manual shows the probability distribution histograms
for this problem exactly as I have described above.
Shouldn't the total area under the distribution equal one?
Sheila King
[EMAIL PROTECTED]
http://www.thinkspot.net/sheila/
http://www.k12groups.org/
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