What is meant by probability mass function?

Definition. A probability mass function (pmf) is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value.

Why is it called a probability mass function?

This is just the same thing as a pmf. The name stems from the fact that there are a finite number of outcomes and and so we can represent these outcomes and their associated probabilities in a finite table.

What is probability mass function for Poisson distribution?

Probability Mass Function. The Poisson distribution is used to model the number of events occurring within a given time interval. The formula for the Poisson probability mass function is. p(x;\lambda) = \frac{e^{-\lambda}\lambda^{x}} {x!} \mbox{ for } x = 0, 1, 2, \cdots.

What is probability mass function of binomial distribution?

The binomial probability mass function is a very common discrete probability mass function that has been studied since the 17th century. It applies to many experiments in which there are two possible outcomes, such as heads–tails in the tossing of a coin or decay–no decay in radioactive decay of a nucleus.

What is the difference between a probability mass function and a cumulative mass function?

The probability density function (PDF) is the probability that a random variable, say X, will take a value exactly equal to x. Whereas, for the cumulative distribution function, we are interested in the probability taking on a value equal to or less than the specified value. …

What are the two basic properties of probability mass function?

The (probability) mass function of a discrete random variable X is fX(x) = P{X = x}. The mass function has two basic properties: • fX(x) ≥ 0 for all x in the state space. ∑x fX(x) = 1. fX(1) = P{X = 1} = P{H} = p fX(2) = P{X = 2} = P{TH} = (1 − p)p fX(3) = P{X = 3} = P{TTH} = (1 − p)2p …