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Unit 4, Probability Distribution - Coggle Diagram
Unit 4, Probability Distribution
Intro to Probability
Probability:
The measure of the possibility of an event to happen
Simulation:
An experimental to model random events, matching closely to the real world situation
Steps in performing a simulation:
-State
-Plan
-Do
-Conclude
Example model on how to perform a simulation:
-Starting at line..., and move every 'n' digit
-Circle the number if it represent a....
-Cross out the number if it represent a...
-Stop when 'n' number of digits are collected
-Record the # of (result) out of 'n'
Be sure to include a KEY
If the result probability is
less than
the significant p-value(0.05), it shows that we
do have
convincing evidence to go against the claim
If the result probability is
greater than
the significant p-value, it shows that we
do not have
convincing evidence to go against the claim
Calculating Probability Distribution
Probability Distribution Table
X: #|.# |
P(X): #|.# |
1-Var Stats(List, FreqList, Calculate)
Strategies for solving probability
Tree Diagram:
-Lots of probability sequential
Formula:
-Probability Distribution
-Check for independence
Venn Diagram:
-Probability between two categories that might over lap
Two way table:
-When two events are mutually exclusive
-Check for independent/dependent
Simulation:
-Testing the probability of an occurring sample by chance
Binomial and Geometric Distribution:
-BINS
-Fixed trials-> Binomial
-Not fixed-> Geometric
Binary
: Yes/No
Independent
: Independence
Number
: Trials
Success:
Probability
Binomial and Geometric Distributions
Binomial Distribution
: The number of trials and the probability of success
Binomial pdf/cdf
mean=np
Std. dev.=√npq
Geometric Distribution:
The probability of the number of attempts needed to get the first success in a series of trials with two possible outcome
Geometric pdf/cdf
mean=1/p
Std. dev.=(√1-p)/p
All Geometric Distribution have a right skewed graph
Interpreting mean and Standard Deviation.
Ex: On average, it will take "mean #" of "
__
", and this is typically off by "standard deviation #"
Combining and Transforming Random Variables
Combining Random Variables
Ex: If coconuts are
packed 5 per box for shipment,
calculate the mean and standard deviation for the amount of fruit per coconut
Transforming Random Variables
Ex: If each pound of coconut
produces 5 ounces of fruit
, calculate the mean and standard deviation for the amount of fruit per coconut
Z-scores are not affected by transformations
Example problem:
Weights of coconuts have a mean of 3.2 pounds with a standard deviation of 0.7 pounds
Add/Subtract or Multiply/Divide measures of center and location
Mean, Median, Min, Max, Q1, Q3
Does not change the shape or spread of the measure
IQR, standard deviation, range
