Short and brief summary of Probability Distributions according to the IB AIHL syllabus. Probability distributions and testing, along with instructions on how to use with a graphic calculator
RANDOM VARIABLES PROBABILITY DISTRIBUTIONS
A random variable represents the possible outcomes T's thusCE Varo
which occur for a random experiment X p n poi xp gggq pas
poisson or poissoncase
Discrete Random Continuous Random ionaitionsforpoissonexperiments
a variable o numberofoccuranceof an event ingiveninterval
o average rate ofoscurance isconstantthroughout interval
p
o occurancesareindependentofeachother
mean variance standarddeviation
it x Poex then
ex varix a
x has distinctset of possible x has possible values in standarddeviation o WI
values which are counted some interval on the number Tisaplus ee
line which are measured
pot probabilitydistribution edf cumulativedistribution
ProbabilityDistributions for any randomvariable there is function function
a correspondingprobability of distribution whichdescribes Pi X x P x is
theprobability that the variable will take any particular
value s se which is denoted as Pax x
IONTINUOUSPROBABILITY DISTRIBUTION
DISCRETE PROBABILITY DISTRIBUTIONS probabilitydensityfunction assigns
ingeneral theexpectationforrandomvariable x is
El x Xi l pix ki
in gambling we say a game is fair if E x o
additionally
BINOMIALDISTRIBUTION rate ofsuccess in n trials pix at Sa fix ax o
probability of 184Plusce rare distr p la e x et lab fix dx
X N B In p success binompate or binomedfl
NORMALDISTRIBUTION
numberoftrials itfrobabilityofsuccess Tisaplus ce ingivars
conditionsforbinomialexperiments x value
o n trials m mean
o a possibleoutcomes success or failure
ymean o standarddeviation
a pisuccess is the same for all trials retailare t
characteristicsof
t eesuccess normal distribution a symmetrical
mean variance standarddeviation i meanmedianmode are equal
if x n Ben p then Ti84 tips
mean ex np finding probabilities finding x givenprobability
variance o npci p normalpass normalsay noinvnorms
g gg
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