What is the Difference Between Discrete and Continuous Probability Distributions?
🆚 Go to Comparative Table 🆚The main difference between discrete and continuous probability distributions lies in the nature of the values that the random variables can take.
Discrete probability distributions are characterized by:
- A finite or countable number of possible values for the random variable.
- Each possible value of the discrete random variable can be associated with a non-zero probability.
- Probabilities are assigned to specific values in the distribution, for example, "the probability that the web page will have 12 clicks in an hour is 0.15".
- Discrete distributions are often presented in tabular form.
Examples of discrete probability distributions include the binomial, geometric, and Poisson distributions.
Continuous probability distributions are characterized by:
- A range or interval of possible values for the random variable, with an infinite number of values within that range.
- The probability associated with any particular value of a continuous distribution is null.
- Continuous distributions are described in terms of probability density, which can be converted into the probability that a value will fall within a certain range.
Examples of continuous probability distributions include the uniform and normal distributions.
In summary, discrete probability distributions involve countable values with non-zero probabilities assigned to each value, while continuous probability distributions involve an infinite number of values within a range, with probabilities associated with the likelihood of a value falling within a specific range rather than at a specific value.
Comparative Table: Discrete vs Continuous Probability Distributions
The main difference between discrete and continuous probability distributions lies in the nature of the values that the random variable can take. Here is a table summarizing the differences between discrete and continuous probability distributions:
| Feature | Discrete Probability Distributions | Continuous Probability Distributions |
|---|---|---|
| Values | Can only take on certain values, usually integers (countable) | Can take on any value within a specified range (uncountable) |
| Examples | - Binomial distribution: used for a process with two possible outcomes - Geometric distribution: determines the probability associated with the number of trials - Poisson distribution: measures the probability that a given number of events will occur within a specified time | - Uniform distribution: represents variables that are evenly distributed over a range - Normal distribution: commonly used to represent continuous data, such as height or weight |
A discrete distribution can always be presented in tabular form, with each possible value of the discrete random variable associated with a non-zero probability. In contrast, a continuous probability distribution has an infinite number of possible values, and the probability associated with any particular value is null. Continuous distributions are usually described in terms of probability density, which can be converted into the probability that a value will fall within a certain range.
- Discrete vs Continuous Distributions
- Discrete vs Continuous Data
- Discrete vs Continuous Variables
- Discrete Function vs Continuous Function
- Random Variables vs Probability Distribution
- Probability Distribution Function vs Probability Density Function
- Poisson Distribution vs Normal Distribution
- Gaussian vs Normal Distribution
- Binomial vs Normal Distribution
- Continuous vs Discontinuous Variation
- Continuous vs Discrete Spectrum
- Discrete vs Discreet
- Probability vs Statistics
- Probability vs Chance
- Probability vs Odds
- Probability vs Possibility
- Likelihood vs Probability
- Continuous vs Continual
- Dispersion vs Diffusion