Discrete Probability Distribution

Definition

A discrete probability distribution is a probability distribution that describes the probability of a discrete random variable taking on a specific value. It is a mathematical function that assigns probabilities to each possible outcome of a discrete random variable.

5 Must Know Facts For Your Next Test

1. Discrete probability distributions are used to model situations where the random variable can only take on a finite or countably infinite number of distinct values.
2. The probability mass function (PMF) is the key function used to describe a discrete probability distribution, as it gives the probability of each possible outcome.
3. Discrete probability distributions are commonly used in the Hypergeometric, Poisson, and Binomial distributions, which are all special cases of the general discrete probability distribution.
4. In a discrete probability distribution, the sum of all probabilities must equal 1, as the random variable must take on one of the possible values.
5. Discrete probability distributions are often used in statistical inference, decision-making, and probability modeling in various fields, such as finance, biology, and engineering.

Review Questions

• Explain how the concept of a discrete probability distribution is related to the Hypergeometric distribution.
  • The Hypergeometric distribution is a specific type of discrete probability distribution that models the number of successes in a fixed number of trials without replacement from a finite population. The Hypergeometric distribution is a discrete probability distribution because the random variable (the number of successes) can only take on a finite set of integer values. The probability mass function of the Hypergeometric distribution is used to calculate the probabilities of the different possible outcomes, which is a key characteristic of a discrete probability distribution.
• Describe the relationship between the Poisson distribution and the concept of a discrete probability distribution.
  • The Poisson distribution is another example of a discrete probability distribution. The Poisson distribution models the probability of a given number of events occurring in a fixed interval of time or space, given that these events occur with a known constant mean rate and independently of the time since the last event. The Poisson distribution is a discrete probability distribution because the random variable (the number of events) can only take on non-negative integer values. The probability mass function of the Poisson distribution is used to calculate the probabilities of the different possible outcomes, which is a key characteristic of a discrete probability distribution.
• Analyze how the concept of a discrete probability distribution is applied in the context of the Playing Card Experiment (Discrete Distribution).
  • The Playing Card Experiment, which is covered in the Discrete Distribution topic, is an example of a discrete probability distribution. In this experiment, the random variable is the suit of a randomly drawn playing card, which can only take on one of four discrete values (Spades, Hearts, Diamonds, or Clubs). The probability mass function is used to calculate the probabilities of each possible suit being drawn, as the random variable is discrete and can only take on a finite set of values. This demonstrates the key characteristics of a discrete probability distribution, where the random variable is discrete, the probabilities are calculated using the probability mass function, and the sum of all probabilities equals 1.

Related terms

Probability Mass Function (PMF):

The probability mass function (PMF) is a function that gives the probability that a discrete random variable is exactly equal to some value.

Discrete Random Variable:

A discrete random variable is a random variable that can take on only a countable number of distinct values, often integers.

Bernoulli Distribution: The Bernoulli distribution is a discrete probability distribution that takes value 1 with probability $p$ and value 0 with probability $1-p$, where $p$ is the success probability.