ISyE 2027 Final Exam
probability mass function (pmf) - ✔️✔️p(a) = P(X=a)
-The pmf of a discrete random variable gives the probability that the random variable
will equal a given value
cumulative distribution function - ✔️✔️SOS
F:R --> [0,1]
Bernoulli distribution - ✔️✔️success or failure
X=1 success
X=0 failure
P(1) = P(X=1) = P
P(0) = P(X=0) = 1-P
Binomial distribution - ✔️✔️Let X represent the number of successes in n trials
X~Bin(n,p)
sequence of Bernoullis
Geometric distribution - ✔️✔️Let X equal the number of trials until a success occurs
Poisson random variable - ✔️✔️A random variable X, taking on values 0,1,2,3... is
poisson w parameter λ for some λ>0
counting process
counts events in a time period
exponential random variable - ✔️✔️time until some event occurs
Discrete uniform distribution - ✔️✔️sos
probability is... - ✔️✔️starting with an animal and figuring out what footprints it will
make
statistics is... - ✔️✔️seeing a footprint and guessing the animal
disjoint - ✔️✔️A ∩ B = ∅ therefore P(A|B) = 0
independence - ✔️✔️P(A|B) = P(A)
P(A|B) - ✔️✔️P(A∩B)/P(B)
probability mass function (pmf) - ✔️✔️p(a) = P(X=a)
-The pmf of a discrete random variable gives the probability that the random variable
will equal a given value
cumulative distribution function - ✔️✔️SOS
F:R --> [0,1]
Bernoulli distribution - ✔️✔️success or failure
X=1 success
X=0 failure
P(1) = P(X=1) = P
P(0) = P(X=0) = 1-P
Binomial distribution - ✔️✔️Let X represent the number of successes in n trials
X~Bin(n,p)
sequence of Bernoullis
Geometric distribution - ✔️✔️Let X equal the number of trials until a success occurs
Poisson random variable - ✔️✔️A random variable X, taking on values 0,1,2,3... is
poisson w parameter λ for some λ>0
counting process
counts events in a time period
exponential random variable - ✔️✔️time until some event occurs
Discrete uniform distribution - ✔️✔️sos
probability is... - ✔️✔️starting with an animal and figuring out what footprints it will
make
statistics is... - ✔️✔️seeing a footprint and guessing the animal
disjoint - ✔️✔️A ∩ B = ∅ therefore P(A|B) = 0
independence - ✔️✔️P(A|B) = P(A)
P(A|B) - ✔️✔️P(A∩B)/P(B)
