2. Discrete and Continuous Distributions
• Random Variable: It is a numerical description of the
outcome of an experiment.
• What is Experiment: A process that generates well defined
outcomes.
• Discrete Random Variable: A random Variable that may
assume either a finite no of values or an infinite sequence of
values is referred to as a discrete random variable.
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4. Contd..
• Continuous Random Variables
A Random variable that may assume any numerical value in an
interval or collection of intervals is called a continuous
random variable. Experimental outcomes based on
measurement scales such as time, weight, distance and
temperature can be described by continuous random
variables.
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5. Binomial probability function
Binomial probability function
F(x) is
• n = number of trials
• k = number of successes
• n – k = number of failures
• p = probability of success in
one trial
• q = 1 – p = probability of
failure in one trial
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6. Poisson Probability Distribution
A discrete random variable that is often useful in estimating the
number of occurrences over a specified interval of time or
space. For example: the random variable of interest might be
the no of arrivals at a car wash in one hour or the no of leaks
in 100 miles of pipeline.
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8. Geometric distribution
If the probability of success is 0.35, what is the probability that
the first success will be on the 5th trial?
dgeom (4 ,0.35)
[1] 0.06247719
dgeom gives the density (or probability mass function for
discrete variables), pgeom gives the distribution function
and rgeom generates random deviates. This is true for the
functions used for Binomial, Poisson and Normal
calculations as well.
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9. Binomial distribution
If the probability of success is 0.35, what is the probability of 3
successes in 5 trials?
dbinom (3 ,5 ,0.35)
[1] 0.1811469
at least 3 successes in 5 trials?
sum( dbinom (3:5 ,5 ,0.35) )
[1] 0.2351694
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10. Poisson distribution
The number of track accidents per week in a small city has
Poisson distribution with mean equal to 3. What is the
probability of two accidents in a week?
dpois (2 ,3)
[1] 0.2240418
at most one accident in a week?
sum( dpois (0:1 ,3) )
[1] 0.1991483
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11. Normal distribution
Scores on an exam are distributed normally with a mean of 65
and a standard deviation of 12. What percentage of the
students have scores
• below 50
pnorm (50 ,65 ,12)
[1] 0.1056498
• between 50 and 70?
pnorm (70 ,65 ,12) -pnorm (50 ,65 ,12)
[1] 0.5558891
What is the 90th percentile of the score distribution?
qnorm (.90 ,65 ,12)
[1] 80.37862
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