Question

The counterpart of probability mass function is:
(a)Probability destruction
(b)Probability density function
(c)Distribution function
(d)None of these

Answer 1

Hint – In this question use the basics of probability mass function as it is considered in the context of the discrete probabilities and it is also called as discrete density functions. Since in probability mass function we are concerned with discrete random variables so the counterpart should include continuous random variables. This will help solve the problem.

Complete step-by-step answer:
Probability mass function (PMF)
As we know all probability mass function (PMF) always refers to discrete probabilities i.e. it is the probability distribution of a discrete random variable, and provides the possible values and their associated probabilities.
Due to this it gives a probability that a discrete random variable is exactly equal to some value.
Sometimes it is called a discrete density function.
It is the primary means of defining a discrete probability distribution and such functions either exist for scalar or multivariate or multi vector random variables whose domain is discrete.
So this is called a probability mass function (PMF).
Now the counter part of the probability mass function (PMF) is the opposite term of the probability mass function (PMF) i.e. probability mass function (PMF) is defined for discrete random variable so the counter part or the opposite of the PMF is defined for continuous system i.e. continuous random variable or it is known as or defined as probability density function.
So the counter part of the probability mass function (PMF) is the continuous random variable which is defined as probability density function (PDF).
So this is the required answer.
Hence option (B) is the correct answer.

Note – Probability mass function is very important and has a large number of applications in mathematics, it is used to calculate mean and even variance that is the measure of randomness for a discrete distribution moreover it also finds applications in binomial and Poisson’s distribution.