Probability Distribution. Sec: 6.1. New Vocabulary:. Random Variable; A random variable is the numerical measurement of the outcomes of a random phenomenon. Examples: Role of a die Drawing cards Work hours of randomly selected person Score of a random game of soccer
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Recall: To find the mean we need to add up all the values and divide by the number of values that occur.
But how many values are there?
How can we make this work?
According to our table we will have 21 out of 100 students that have half a year left, 31 of 100 with one year left, and so on.
We can find μ by letting the number of values be equal to 100 and use the percentages as the number of times they occur.
So, the Average student has 1.31 years left until they get there degree.
With few intervals the graphs will be wrought even will a large sample.
But as the intervals shrink the graph will become increasingly smooth.
Until finally becoming the smooth curve.
The probability of an interval is equal to the area under the curve over that interval.
P(A)=.15 = 15%
What is the area under the whole curve?
P(B) = 1
Area = 1 unit
It is uncommon for data to be perfectly normal. Either the data comes from to small of a sample, or the discrete intervals make the image jagged, or the data was just never normal to begin with.
We will however use the normal curve for many of our models that are “nearly” normal.
It is simply to powerful of a tool to worry about it fitting “just right”.
And we can get surprisingly accurate results from distributions that are quite a bit off from normal. We just need to be careful and aware.
HW: 6.1; 6, 19*, 23*, 27, 31,33