Geometric Distribution Calculator

Step-by-Step Guide to Using the Geometric Distribution Calculator

This guide will walk you through the process of using the Geometric Distribution Calculator to evaluate various statistical measures associated with the geometric distribution. Follow these steps to obtain the Probability Mass Function, Cumulative Distribution Function, and other significant statistical values.

Step 1: Input the Probability of Success

The first field you need to fill is the Probability of Success (p). This is the probability of a success on any given trial and should be a decimal value between 0 and 1.

• Locate the input field labeled Probability of Success (p).
• Enter a value between 0 and 1. For example, if you expect a success rate of 5%, enter 0.05.
• The input supports values with up to two decimal places.

Step 2: Enter the Number of Trials

Next, you need to specify the number of trials until the first success occurs, labeled as Number of Trials until First Success (k).

• Find the input field labeled Number of Trials until First Success (k).
• Enter a whole number greater than 0, representing the trial at which the first success is observed.
• For example, if you’re interested in the probability that the first success happens on the 3rd trial, enter 3.

Step 3: Interpret the Results

Once you’ve provided the necessary inputs, the calculator will automatically compute and display several key statistical measures associated with the geometric distribution. Know what each value represents:

• Probability Mass Function P(X = k): This value represents the probability of getting the first success on the kth trial. It is calculated using the formula: probability * (1 - probability)^(trials - 1).
• Cumulative Distribution Function P(X ≤ k): This results show the probability that the first success will occur on or before the kth trial. The calculation follows: 1 - (1 - probability)^trials.
• Expected Value (Mean): This indicates the average number of trials expected before achieving the first success. It is calculated using: 1 / probability.
• Variance: This is a measure of the data’s dispersion, calculated as: (1 - probability) / probability^2.
• Standard Deviation: This is the square root of the variance, which provides insight into the variability around the expected value. The formula is: sqrt((1 - probability) / probability^2).

Conclusion

Now that you have interpreted the results, you can use these statistical measures to analyze phenomena that follow a geometric distribution. Adjust the inputs as needed to explore different scenarios and deepen your understanding of geometric distributions.