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Cheat-Sheet 02 4x6" Statistics

1. This document discusses key probability concepts including classical, subjective, and relative frequency approaches to probability. It also covers probability rules, odds, addition and multiplication rules, conditional probability, permutations, combinations, probability distributions, the binomial distribution, the normal distribution, and the central limit theorem. 2. Formulas are provided for permutation, combination, binomial probability, standard normal distributions, and the central limit theorem. 3. Examples of how to use the normal approximation to the binomial are given to calculate probabilities.

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Eduardo Steffens
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224 views2 pages

Cheat-Sheet 02 4x6" Statistics

1. This document discusses key probability concepts including classical, subjective, and relative frequency approaches to probability. It also covers probability rules, odds, addition and multiplication rules, conditional probability, permutations, combinations, probability distributions, the binomial distribution, the normal distribution, and the central limit theorem. 2. Formulas are provided for permutation, combination, binomial probability, standard normal distributions, and the central limit theorem. 3. Examples of how to use the normal approximation to the binomial are given to calculate probabilities.

Uploaded by

Eduardo Steffens
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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1. Relative Freq.: Conduct procedure and count the number of times that it occurs.

2. Subjective Prob.: P(A) is estimated by using knowledge of relevant circumstances.


3. Classical Approach: P(A) = (# ways A occur)/(# simple events)
Probability Rules 0 P(x) 1 and P(x) = 0 (impossible) P(x) = 1 (certain)
Unusual Event P(A)
0.05
Law of Large Number: As a procedure is repeated many times, the relative freq. prob. tends to
approach the actual prob.
)/(P(A) a:b
Odds Actual odds against event A happening P( A

)
Actual odds in favor of event A happening P(A)/(P( A
Pay-off odd against A = not profit : amount bet
Addition Rule Mutually Exclusive P(A or B) = P(A)+P(B)
Not Mutually Exclusive P(A or B) = P(A)-P(B)
Multiplication Rule Independent Event (Two events are independent if when A occurs, the prob B
occurs is not affected)
If the sample size is no more than 5% of the population, treat the selections as independent events
P(A and B) = P(A)*P(B)
Dependent Event: P(A and B) = P(A)*P(B\A)
(P(B\A) Conditional Probability is the probability that B occurs given A has occurred P(B\A)=P(A and
B)/P(A))
Complements P(at least x) = 1-P(at most x-1)
Permutation (order matters) 1. There are n different items available 2. Select r of the n items r<n 3.
Rearrangement of the same items to be different sequences
nPr=

n!
( nr ) !

Combination (order doesnt matter) 1. There are n different items available 2. Select r of the n items
r<n 3. Rearrangement of the same items to be same sequences

nCr=

hh

n!
( nr ) ! r !

Probability Distribution
(requirements: 1) P(x) = 1 and 2) 0 x 1)
Unusually high # if: P(x or more) 0.05 or +2
Unusually low # if: P(x or less) 0.05 or
+2
Binomial Prob Distribution
(requirements: 1) Procedure has a fixed # of trials n; 2) Trials are independent [sampling with
replacement or sample 5% of pop.); 3) Each trial must have two categories; and 4) The prob of
success remains the same)
P(exactly x=__) = binomPdf();
P(at least x=__) = 1-P(at most x-1) = 1-binomCdf();
P(at most x=__) = binomCdf();
Density Curve Continuous Random Variable (requirements: 1) The area under the curve equals 1;
2) Density curve sits on or above x-axis. Vertical height of zero or above.)
Uniform Distribution Probability Graph is a rectangle
Standart Normal Distribution Graph is bell-shaped
1. Sketch the normal curve, and label and ; 2. Label x values and shade the area desired; 3. Use the
calculator to find area (probability)
The functions used in the calculator is normalCdf() and invNorm()
The Central Limit Theorem:

x =

and

x = / n

1) If the original population is normally distributed, then for any sample size, the sample means are
normally distributed
2) If the original population is not normally distributed, then for a sample n>30, the sample means are
normally distributed
Normal as Approximation to Binomial (requirement: 1) Sample is a SRS; 2) np 5; 3) nq 5)
If r is left point of an interval x = r-0.5
>>> P(r __ ) = P(x __-0.5) = normalCdf()
If r is right point of an interval x = r+0.5 >>> P(r __ ) = P(x __+0.5) = normalCdf()
Ex) 1000 tickets are sold at $2 each for a prize valued at $650. What is the expected value of gain if a
person purchases one ticket?
GAIN
P(x)

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