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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. 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 $P(X \leq 3) = 0.86878$ 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 $\lambda = 3$, then $P(X \leq 3) = 0.6472319$ 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 $P(X \leq 2) = 0.9772499$. In addition the value of c in P(X < c) = .95 is 1.644854.
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Next:Resampling Up:Statistics and Data Analysis Previous:Plots

2000-08-21