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Final

Formula Sheet for Exam

2 Pages
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Department
Economics for Management Studies
Course Code
MGEB11H3
Professor
Vinh Quan

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Required Conditions for a Discrete
Probability Function
:E;2:T;Rr :EE;Ã2:T;Ls
Discrete Uniform Probability Function
2:T;Ls
J
n = # of values the random variable
may assume
Expected Value of a Discrete Random
Variable
':T;LäLÍT2:T;
The mean value for the random
variable.
Variance of a Discrete Random
Variable
8=N:T;Lê6LÍ:TFä;6B:T;
Number of Experimental Outcomes
Providing Exactly x Successes in n
Trials
@J
TALJè
Tè:JFT;è
*0! = 1
Probability of a Particular Sequence of
Trial Outcomes with x Successes in n
Trials
Lë:sFL;:á?ë;
Binomial Probability Function
B:T;LJè
Tè:JFT;è
Lë:sFL;:á?ë;
n = trials | x = successes
Expected Value for the Binomial
Distribution
':T;LäLJL
Variance for the Binomial Distribution
8=N:T;Lê6LJL:sFL;
Poisson Probability Function
B:T;LäëA?
Tè
f(x) = the probability of x occurrences
in an interval
Poisson Distribution
x äLê6
Uniform Probability Density Function
B:T;L]s
>F=BKN=QTQ>
rAHOASDANA
Uniform Continuous Probability
':T;L=E>
t
8=N:T;L:>F=;6
st
Normal Probability Density Function
B:T;Ls
ê¾tèA?:ë?;.6.
Normal Probability Distribution
x 68.3% of the values of a normal
random variable are within plus
or minus one standard
deviation of its mean.
x 95.4% of the values of a normal
random variable are within plus
or minus two standard
deviation of its mean.
x 99.7% of the values of a normal
random variable are within plus
or minus three standard
deviation of its mean.
Standard Normal Probability
Distribution
äLráêLs
Standard Normal Probability Density
Function
B:T;Ls
¾tèA?í.6
Converting to the Standard Normal
Random Variable
VLTFä
ê
Normal Approximation of Binomial
Probabilities
äLJL
êL¥JL:sFL;
Expected Value of
%
':T§;Lä
':T§; = the expected value of T§
ä = the population mean
Standard Deviation of
%
Finite Population
êë§L¨0FJ
0Fslê
¾Jp
Infinite Population
êë§Lê
¾J
êë§Lthe standard deviation of T§
ê = the standard deviation of the
population
n = the sample size
N = the population size
Use the following expression to
compute the standard deviation of T§
êë§Lê
¾J
whenever
1. The population is infinite; or
2. The population is finite and the
sample size is less than or equal
to 5% of the population size;
that is, á
Ç
Qrärwä
Central Limit Theorem
In selecting simple random samples of
size n from a population, the sampling
distribution of the sample mean T§ can
be approximated by a normal
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Description
Required Conditions for a Discrete Poisson Probability Function Converting to the Standard Normal ? Probability Function * 6 L ) Random Variable :- : 6 4 H :-- : 6 L I 6 6 . 8 L f(x) = the probability of x occurrences Discrete Uniform Probability Functionin an interval I Normal Approximation of Binomial :6 L Probabilities J Poisson Distribution $ L JL n = # of values the random variable N L L L:I . L; may assume Uniform Probability Density Function Expected Value of Expected Value of a Discrete Random I Variable * 6 L] > . = *KN= 3 6 3 > 6 L H)0O)5,)N) 6 L L6 :6; 6 = the expected value of 6 = the population mean Uniform Continuous Probability The mean value for the random = - > variable. 6 L Standard Deviation of J :> . =; $ Finite Population Variance of a Discrete Random &=N 6 L IJ L . J l F Variable . I J &=N 6 L L:6 . ; *:6;$ Normal Probability Density Function I Infinite Population * 6 L ) ? ? ; $ J L Number of Experimental Outcomes J Providing Exactly x Successes in n Normal Probability D
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