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STAT131 Week 6 L1b Introduction to Continuous Random Variables. Anne Porter email@example.com. Sample. Population Model Discrete Random Variable. Review: Sample and Model Centre and spread . Centre Spread Variance Spread Standard Deviation. S x 2. S x. Binomial~ (n,p).
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DR VariableReview Discrete Random Variables & Specific case of the Binomial
There is no possible measure between the points on the scale
Examples of discrete random variables:
The number of successes in n fixed trials - Binomial
The count of some event per unit time
The set of possible values of the RV is neither finite
not countably infinite.
Sample space is the values that the random variable can
possibly take on.
That is the battery does not ever work,
0 units of time, to possibly working for ever
Note that in some instances we don’t actually
need to estimate spread eg Poisson where Mean = Variance
Hence we are interested in intervals of values
Example: P( 10 <X < 20)
Is there any difference in answer for these
No because the probability of exactly equalling a constant
given a continuous random variable is
Test the lifetime of a number of batteries , that is, use the relative frequency approach.
By summing the areas of all the individual bars
By finding the area of the smallest possible bars and as the
size decreases it becomes finding the integral over the
and b is given by
the pdf defined as illustrated, y=1/2 0<x<2. Find the area under the function by using
Area=2x0.5=1 square unit
is found for
How did we do this?
By use of symmetry
How do we calculate the mean
For a discrete random variable?
How then do we calculate the mean
for a continuous random variable?
Histogram (observed & expected )
- The bins can have different widths
- The bins can start in different positions
- This will affect the numbers
and the numbers expected in cells
- The expected count in each > 5
d=g-p-1 where p is the number of parameters estimated
So for the Poisson () we have one parameter