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Probability
Probability computations for some discrete and continuous distributions
are performed by choosing probability from the analysis menu and
clicking "Submit". No data is needed for probability computations. The
particular probability(ies) desired may then be chosen from the list of
probability statements provided. The following are the probabilities that
are pertinent to this course.

Cumulative binomial  needs the number of trials (n), number of
successes (k) and probability of success for each trial (p).

Binomial density  needs the number of trials (n), number of successes
(k) and probability of success for each trial (p).

Cumulative Poisson  needs number of occurrences (k) and the expected
number of occurrences ()

Poisson density  needs number of occurrences (k) and the expected
number of occurrences ()

Cumulative normal  the default is the standard normal distribution.
Consider the following inputs.
The corresponding output is
Rweb:> # CUMULATIVE BINOMIAL DISTRIBUTION
Rweb:> pbinom(3, 5, .45)
[1] 0.86878
Rweb:> # BINOMIAL PROBABILITY
Rweb:> dbinom(3, 5, .45)
[1] 0.2756531
So, if X is a random variable which follows the binomial distribution
with n = 5 and p = 0.45, then
and P(X = 3) =
0.2756531.
Rweb:> # CUMULATIVE POISSON DISTRIBUTION
Rweb:> ppois(3, 3)
[1] 0.6472319
Rweb:> # POISSON PROBABILIY
Rweb:> dpois(3, 3)
[1] 0.2240418
So, if X is a random variable which follows the Poisson distribution
with ,
then
and P(X = 3) =
0.2240418.
Rweb:> # CUMULATIVE NORMAL DISTRIBUTION
Rweb:> pnorm(2, 0, 1)
[1] 0.9772499
Rweb:> # NORMAL PERCENTAGE POINT
Rweb:> qnorm(.95, 0, 1)
[1] 1.644854
If X follows the standard normal distribution, then .
In addition the value of c in P(X
< c) = .95 is 1.644854.
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