Equiprobable Distribution

Definition

An equiprobable distribution is a probability distribution where all possible outcomes or events have an equal chance of occurring. In other words, each outcome has the same probability of being observed or selected.

5 Must Know Facts For Your Next Test

1. An equiprobable distribution is a special case of the uniform distribution, where the random variable has a constant probability density function over a finite interval.
2. In an equiprobable distribution, the probability of any one outcome occurring is the same as the probability of any other outcome occurring.
3. Equiprobable distributions are often used to model situations where there is no inherent bias or preference for any particular outcome, such as in the roll of a fair die or the flip of a fair coin.
4. The probability mass function (PMF) for an equiprobable discrete distribution is a constant value across all possible outcomes.
5. The cumulative distribution function (CDF) for an equiprobable distribution is a linear function, increasing at a constant rate across the range of the random variable.

Review Questions

• Explain how an equiprobable distribution differs from a non-equiprobable distribution.
  • In an equiprobable distribution, all possible outcomes have an equal probability of occurring, whereas in a non-equiprobable distribution, the probabilities of the different outcomes vary. For example, in the roll of a fair die, each of the six possible outcomes (1, 2, 3, 4, 5, 6) has an equal probability of 1/6, making it an equiprobable distribution. However, in the roll of a biased die, the probabilities of the different outcomes would not be equal, resulting in a non-equiprobable distribution.
• Describe the properties of the probability mass function (PMF) and cumulative distribution function (CDF) for an equiprobable distribution.
  • For an equiprobable discrete distribution, the probability mass function (PMF) is a constant value across all possible outcomes. This means that the probability of any one outcome is the same as the probability of any other outcome. The cumulative distribution function (CDF) for an equiprobable distribution is a linear function, increasing at a constant rate across the range of the random variable. The CDF will have a slope of 1/n, where n is the number of possible outcomes, and will reach a value of 1 at the upper bound of the distribution.
• Explain how an equiprobable distribution is related to the concept of fairness and unbiased decision-making.
  • An equiprobable distribution is often associated with the concept of fairness and unbiased decision-making. When all possible outcomes have an equal probability of occurring, it suggests that there is no inherent bias or preference for any particular outcome. This makes the equiprobable distribution a useful model for situations where fairness and impartiality are important, such as in the roll of a fair die, the flip of a fair coin, or the selection of a winner in a random drawing. By ensuring that all outcomes have an equal chance of being selected, the equiprobable distribution promotes a sense of fairness and objectivity in the decision-making process.

Related terms

Uniform Distribution: A continuous probability distribution where the random variable has an equal likelihood of taking on any value within a given interval.

Probability Mass Function: A function that gives the probability that a discrete random variable is exactly equal to a particular value.

Cumulative Distribution Function: A function that gives the probability that a random variable is less than or equal to a particular value.