Random Variable
A random variable is a variable which contains numeric values.
Random variable is the subject to randomness i.e it can take on different values and each value of a random variable have a probability associated with it.
It is denoted with X.
Types of random variable :
Discrete Random Variable
A discrete random variable X is the random variable that consists of countable values.
Examples : number of balls in a bag, number of students in a class etc.
The elements of discrete random numbers are isolated i.e they are separate and individual.
Probability Mass Function (PMF)
If X is discrete random variable having x1, x2, x3…xn as its elements and we find the values of P(X = x1), P(X = x2), P(X = x3)…P(X = xn), then the functions P(X = x) for x = x1, x2, x3…xn is called as probablity mass function.
Example :
The following table and graph shows the PMF for an experiment :
Continuous Random Variable
A random variable X that contains infinite number of values between a given interval is known as continuous random variable.
Example : Height of a person, Price of a commodity etc.
Probability Density Function (PDF)
Probability density function (PDF), in statistics is a function whose integral is calculated to find probabilities associated with a continuous random variable.
When the PDF is plotted, the area under the curve will indicate the interval in which the continuous variable will fall.
Example :
Cummulative Density Function (CDF)
The cumulative distribution function is a function derived from the probability density function for a continuous random variable.
It is the probability that the variable takes a value less than or equal to x.
Example :
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