There are many famous continuous probability distributions, such as the normal and exponential distributions. How can we get access to them in software, to compute the probability of a value/values occurring?
- How to generate random values from a distribution
- How to plot continuous probability distributions
- How to plot discrete probability distributions
Because R is designed for use in statistics, it comes with many probability distributions built in. A list of them is online here.
To compute a probability from a discrete distribution, prefix the name
of the distribution with
d (for “density”) and call it as a function on the
value whose probability you want to know, plus any parameters the distrubtion needs.
1 2 3 4 # For a binomial random variable with 10 trials # and probability 0.5 of success on each trial, # what is the probability of exactly 3 successes? dbinom( 3, size=10, prob=0.5 )
1  0.1171875
If you change the prefix to
p, then R will compute the probability up to
the parameter you specify, as in the following example.
1 2 3 4 # For a binomial random variable with 10 trials # and probability 0.5 of success on each trial, # what is the probability of up to (and including) 3 successes? pbinom( 3, size=10, prob=0.5 )
1  0.171875
To compute a probability from a continuous distribution, prefix the
d, just as in the example above. But you can compute only
the probability that a random value will fall in an interval $[a,b]$,
not the probability that it will equal a specific value.
1 2 3 # For a normal random variable with mean μ=10 and standard deviation σ=5, # what is the probability of the value lying in the interval [12,13]? pnorm( 13, mean=10, sd=5 ) - pnorm( 12, mean=10, sd=5 )
1  0.07032514
Consequently, we can also compute:
1 2 pnorm( 13, mean=10, sd=5 ) # the probability of a value < 13 1 - pnorm( 13, mean=10, sd=5 ) # the probability of a value > 13
1 2 3 4 5  0.7257469  0.2742531
Content last modified on 24 July 2023.
- Nathan Carter (firstname.lastname@example.org)
- Elizabeth Czarniak (CZARNIA_ELIZ@bentley.edu)