Department

Economics for Management Studies

Course Code

MGEB11H3

Professor

Vinh Quan

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>

rAHOASDANA

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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