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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.

Next:Resampling Up:Statistics and Data Analysis Previous:Plots

2000-08-21