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Chapter 6 AP Statistics
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Terms in this set (35)
Random Variable
takes numerical values determined by the outcome of a chance process
Probability Distribution
tells us what the possible values of X are and how probabilities are assigned to those values
Discrete Random Variable
has a fixed set of possible values with gaps between them
Continuous Random Variable
takes all values in some interval of numbers
Mean (Expected Value) of a Random Variable
the balance point of the probability distribution density curve or histogram
Mean of a Discrete Random Variable
Variance of a Random Variable
the "average" squared deviation of the values of the variable from their mean
Standard Deviation
the square root of the variance and measures the typical distance of the values in the distribution from the mean
Variance of a Discrete Random Variable
Adding/Subtracting/Multiplying/Dividing Constants to a Random Variable
adding/subtracting changes the mean but not the standard deviation and multiplying/dividing affects both but does not change the shape of the distribution
Linear Transformation
involves adding or subtracting a constant, multiplying or dividing a constant, or both
Y=a+bx
Shape of a Linear Transformation
same as the probability distribution of X is b>0
Center of a Linear Transformation
uy=a+bux
Spread of a Linear Transformation
oy=IbIox
Mean of the Sum of Two Random Variables
the sum of their means
Mean of the Difference of Two Random Variables
the difference of their means
Independent Random Variables
knowing the value of one variable tells you nothing about the other
The Variance of the Sum of Two Independent Random Variables
the sum of their variances
The Variance of the Difference of Two Independent Random Variables
the sum of their variances
Binomial Setting
consists of independent trials of the same chance process, each resulting in success or failure, with probability of success on each trial
Binomial Random Variable
the count X of successes
Binomial Distribution
its probability distribution
Binomial Coefficient
Factorial
n!=n(n-1)(n-2)...(3)(2)(1)
Binomial Probability
Mean of a Binomial Random Variable
Standard Deviation of a Binomial Random Variable
10% Condition
the binomial distribution with trials n and probability p success gives a good approximation to the count of successes in an SRS of size n from a large population containing proportion n of successes as long as the same size n is no more than 10% of the population size N
Normal Approximation
if X is a count of successes having the binomial distribution with parameters n and p, then when n is large, X is approximately Normally distributed with mean np and standard deviation square root of np(1-p)
Large Counts Condition
using normal approximation when np>=10 and n(1-p)>=10
Geometric Setting
consists of repeated trials of the same chance process in which the probability p of successes is the same on each trial, and the goal is to count the number of trials it takes to get one success
Geometric Random Variable
Y when Y= the number of trials required to obtain the first success
Geometric Distribution
its probability distribution
Geometric Probability
Mean of a Geometric Random Variable
uy=1/p
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