There are two candidates in an election where the winner is chosen based on a simple majority. Each of
voters votes for candidate 1 with probability
and for candidate 2 with probability
, where
, so that a voter may choose not to vote for either candidate. When
,
, the probability of one swing vote is:
Probability that a winner won by one vote:
Probability that candidate 1 wins the election:
Probable outcome of the next election:
Average outcome of an election:
Distribute 5 balls among 3 containers, picking each container with equal probability. Find the probability that no container is empty:
Compute the same probability using
SurvivalFunction:
Distribute
balls among
containers with equal probability. Find the probability that no container is empty for different values of
and
:
In calling a customer service center, one of three things may happen: the line is busy with probability 0.4, a caller gets the wrong party with probability 0.1, or a caller gets connected to an agent. Find the probability that a caller calling at 6 different times gets a busy signal 4 times and twice connects directly to an agent:
Find the probability that calling at 6 different times, a caller gets the wrong party at least twice:
Simulate 6 calling attempts done at different times:
In a certain city, out of all 911 calls 30% were requesting an ambulance, 15% were requesting the fire department, and the rest were police requests. Find the probability that in the next 10 emergency calls, 2 will ask for an ambulance, 1 for the fire department, and 7 for police:
Simulate the request distribution for the next 100 calls:
Define a multivariate Polya distribution as a parameter mixture of multinomial distribution:
.
of non-negative integers 
, 
, ..., 
in a multinomial distribution is 
.
can be any non-negative real numbers such that 
.
EXAMPLES
Basic Examples 
Scope 