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AP Statistics: Chapter 7
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Terms in this set (28)
Discrete
Countable
R.V.
Random variable
Random Variable
A Variable whose value is a numerical outcome of a random phenomenon. It is a function that assigns a probability to a numeric outcome experiment
Discrete Random Variable
X, is a random variable that has a countable number of possible values. Can be represented in a histogram or table, but not in a bell curve.
Probability distribution of X looks like...
Probability histogram
Can be used to display the probabilty of a distributin of a discrete R.V.
Continuous Random Variable
X, takes on all values within an interval of numbers. Isn't a set amount of outcomes. Cannot be represented in a histogram or table, but in a bell curve.
Density Curve
Continous R.V.
The area at any given # on a density curve is
0
To be a probability distribution...
1) All values must add to 1
2) All values must be in between 0 and 1
Given
1) Normal
2) SRS
3) n=
4)p=
5)σ=
Probability Notation
N(p, σp)
Z-score formula
z=(p̂-p/ σp)
Expected Value
μx, the mean of a random variable (where X=R.V.)
Mean of a discrete random variable
μx=∑(xi)(pi)
1) xi = every value
2) pi = every probability
When a distribution is symmetric, the mean is...
The center of the distribution (μx = median)
If X is a random variable and Y = a+bx then μy...
=μ(sub)a+bX
If X and Y are 2 random variables then μ(sub)x+y...
=μx+μy
Variance of discrete random variable
σ²x=∑(xi-μx)²(pi)
Standard deviation of a discrete random variable
σx=the square root of ∑(xi-μx)²(pi)
Variance rules
1) Variances always add (because it measures distance, not negative)
2) σ²x+y = σ²x + σ²y
3) σ²x-y = σ²x + σ²y (because they always add)
σx+y =
the square root of σ²x + σ²y
σx+y is not equal to σx + σy because
The variances must always be combined, and rooted, instead of comining the standard devitations
To combine standard deviations and variances, X and Y must be
Independent random variables (so that there is no overlap)
To combine the means, X and Y can be
Independent or dependent
Law of large numbers
1) When there is a small # of observations the mean will be all over the place
2) A larger sample size will settle chaos and the sample value will get closer to μ
Law of large numbers: When n increases, x bar
Gets closer to μ
Law of large numbers proves that...
Averaged results of many independent observations are both stable and predictable
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