Discrete Probability distributions and joint probability distribution
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Course
Probability, random process and Numerical methods
Institution
Kerala Technological University
Provided complete notes on Discrete probability distributions like Binomial, Poisson distribution using statistical tables, Short cuts in using calculator, and also Discrete joint probability distributions, Marginal distributions, expectation and Independence
Probability, random process and Numerical methods
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Discrete Probability
Distribution
Probability function, Distribution function, Mean,
Variance, Problems
, MODULE I
DISCRETE PROBABILITY DISTRIBUTIONS
Defintions:
RANDOM EXPERIMENT: An experiment that can give different outcomes even though it is repeated
under same conditions is called random experiment
SAMPLE SPACE: The set of all possible outcomes of a random experiment is called sample space
denoted by S.
1. Tossing a coin has sample space S={ H, T}
2. Throwing a die S ={ 1, 2, 3, 4, 5, 6}
3. Tossing two coins simultaneously S = { HH, HT, TH, TT}
4. Tossing a coin twice S= { HH, HT, TH, TT}
5. Tossing a coin thrice S= { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Note: When a coin is tossed n times the no. of outcomes is 2n
When a die is thrown n times the no. of outcomes is 6n
Prijimol V B, Assistant Professor, Christ college of Engineering ,
Irinjalakuda
,RANDOM VARIABLE: A variable that assigns a real number to every outcome of a random experimen
called a random variable
Random variables are denoted by capital letters X, Y, Z etc. and its values by small letters as x, y, z, …et
CLASSIFICATION OF RANDOM VARIABLES:
Discrete random variable ( will learn in First module)
Continuous random variable (will learn in Second module)
DISCRETE RANDOM VARIABLE: A random variable that takes only finite discrete number of value
called a Discrete random variable. It is usually an integer value
Eg: 1. No. of accidents on a road = 0, 1 , 2, 3….
2. No. of absentees in a class per day = 0, 1, 2, …..
CONTINUOUS RANDOM VARIABLE: A random variable that takes all possible values in an interva
called Continuous random variable. It is usually any real number in a interval.
Eg. Height, weight, temperature etc
Prijimol V B, Assistant Professor, Christ college of Engineering ,
Irinjalakuda
, PROBABILITY MASS FUNCTION (PMF) OR PROBABILITY FUNCTION OF A DISCRETE
RANDOM VARIABLE
The function P(X = x) = f(x) of a discrete random variable is said to be a PMF if it satisfies the following
two conditions
f(x) ≥ 0
f ( x) 1
It is usually denoted by f(x) or p(x)
PROBABILITY DISTRIBUTION : The probability distribution is the set of values [ x , f(x) ]
CUMULATIVE DISTRIBUTION FUNCTION OR DISTRIBUTION FUNCTION (CDF) OF A
DISCRETE RANDOM VARIABLE
If X is a discrete random variable then its CDF is given by
F ( x) P( X x) f (t ) Add all probabilities upto X x
tx
It is usually denoted by F(x).
Mean= xi pi
i 1
Variance= 2 xi 2 pi 2 Prijimol V B, Assistant Professor, Christ college of Engineering ,
i 1 Irinjalakuda
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