How do we know an event is going to take place? While some use their intuition, however, mathematicians developed a relatively scientific approach towards prediction – probability distribution. While a lot of time probability is confused with statistics, however, a probability distribution identifies the likelihood of different outcomes in an event.
Continuous probability distribution is a type of probability distribution that describes the probability of a continuous random variable taking on a particular value. These types of distributions are used to model things like the height of a person, the time it takes to complete a task, or the distance a car travels.
Dating back to the 18th century, when mathematician Abraham de Moivre first developed the normal distribution, continuous probability distribution has witnessed gradual progress. While in the 19th century, mathematician Pierre-Simon Laplace developed the exponential distribution, which is used to model the time between events, Eric Weibull developed the Weibull distribution, used to model the time to failure of mechanical systems, such as car tires in the 20th century.
Today, continuous probability distributions are an important tool in fields such as statistics, economics, and engineering, and they continue to be developed and refined as our understanding of the world around us grows.
Continuous probability distribution: Explaining the complex term to little learners in a facile manner
Continuous probability can be slightly tricky for young learners to grasp. In the simplest terms, a continuous probability distribution is a way of understanding how likely different things are to happen. Imagine you have a bag of marbles, and each marble is a different color. If you want to understand how likely it is to pick out a certain color of marble, you could use a continuous probability distribution.
First, you would count how many marbles of each color are in the bag. Let’s say there are 10 red marbles, 20 blue marbles, and 30 green marbles. This tells us that it is more likely to pick out a green marble than a red marble because there are more green marbles in the bag.
Next, you could use a graph to show the probability of picking out each color of marble. The graph would have the colors of the marbles on the horizontal axis and the probability of picking out each color on the vertical axis. The probability of picking out a red marble would be 10/60 because there are 10 red marbles out of a total of 60 marbles in the bag. The probability of picking out a blue marble would be 20/60, and the probability of picking out a green marble would be 30/60.
This is similar to how a continuous probability distribution works, except that instead of the colors of marbles, it can be used to understand the probability of any continuous variable, such as height or time. Continuous probability distributions can help us understand and make predictions about uncertain events in the real world.
Continuous probability distribution real-life examples
Probability distributions are divided into two types: discrete and continuous. The latter is applicable in a variety of distributions, which have immense influence in real-world scenarios. Hence, below are real-life examples of the continuous probability distribution.
1. Heights of adult individuals in a population
Height is a measurable variable that can assume any value in a sample or population. As height is a continuous variable, the heights of the adult human population can be modeled by a continuous probability distribution. It is influenced by factors such as genetics and environmental conditions.
2. Test scores in a class or on a standardized test
A test generally has an upper limit of 100 and thus marks can vary between 0-100. As the test scores are a continuous variable that can take any value within a certain range. For instance, students’ scores may take any value such as 56, 75.5, or 32, and can even be in decimals. They are influenced by factors such as student effort and test difficulty.
3. Weight of adult individuals in a population
The exact number of individuals is often in decimal and can even vary on a daily basis between 2-3kg. Hence, weight is a continuous variable that can take any value within a certain range and can be best modeled using the continuous probability distribution. It is influenced by factors such as genetics, diet, and physical activity.
4. Blood pressure in a population
Blood pressure can sometimes rise or fall drastically in the same individual and the value can be absolutely random. Hence, it is a variable that can take any value within a certain range, and it can be best presented with the help of continuous probability distribution. Through the distribution, one can arrange high blood pressure and low blood pressure range. It is influenced by factors such as age, gender, and genetics.
5. Internet download speed
The internet speed can also accelerate or slow down due to different factors. As the speed can assume different values in Mbps, the internet download speed can be modeled through a continuous probability distribution. For example, the internet download speed in a city can be modeled by a normal distribution with a specific mean and standard deviation.
6. Duration of a movie
Different movies have different running times, while short movies could be of 1 hour, commercial movies can range anytime between 2-2.5 hours. The duration of a movie can be modeled through a continuous probability distribution and it would be interesting to note what genres of movies are the shortest or longest. For example, the duration of Hollywood movies can be modeled by a normal distribution with a mean of around 120 minutes and a standard deviation of around 20 minutes.
7. Lifetime of electronic devices
The lifetime of electronic devices may vary from months to years, hence, making it a continuous variable. Their life is influenced by factors such as manufacturing quality and usage conditions. To present their lifetime and predict the ideal range within which they can last, a continuous probability distribution can be used.
8. Wind speeds at a geographical location
Wind speeds are different at every geographical location and they are influenced by factors such as season and local weather patterns. As wind speed is a continuous variable, a continuous probability distribution can better help present and predict the range of wind speed in a location.
9. Daily returns on a stock
Returns on a stock are influenced by factors such as market conditions and company performance. Often the return rate which assumes a quantitative value is unpredictable, and random and can take infinite numbers amongst the real values, hence, it is a continuous variable. Due to the fluctuations in stock prices, the continuous probability distribution is the best to map and predict any changes in stock returns.
10. Rainfall at a particular location
Average precipitation in an area is a given, however, still the amount of rainfall a location receives fluctuates. Therefore, rainfall is a continuous variable and is affected by factors such as season and local weather patterns. Often continuous probability distributions are used to map and predict the average rainfall an area will receive.
Overall, continuous probability distributions are an important tool in statistics and probability theory. They describe the likelihood of different outcomes in a random event and can be used to make predictions, quantify risk, analyze data, and model real-world phenomena. Alongside their long history, important contributions have been made by mathematicians such as Abraham de Motives, Pierre-Simon Laplace, and Eric Weibull. Today, they continue to be important tools in fields such as statistics, economics, and engineering, and they are likely to remain an important part of our understanding of the world around us. Hence, they can also be inculcated through the help of games and activities, to help the kids understand the concept better.