How to Use the Geometric Distribution Calculator?

1. Enter the Probability of Success (p)
Start by inputting the probability of success for a single trial. This value should be between 0 and 1. For example, if there’s a 20% chance of success on each trial, enter 0.2.

2. Specify the Number of Trials (x)
Enter the number of trials you’re interested in. This should be a positive integer. For instance, if you want to know the probability of success on the 5th trial, enter 5.

3. Click the “Calculate” Button
After entering both values, click the “Calculate” button to process your input.

4. Interpret the Results
The calculator will display several key pieces of information:

a) Probability Mass Function (PMF): This shows the probability of achieving the first success exactly on the xth trial.

b) Cumulative Distribution Function (CDF): This indicates the probability of achieving the first success within x trials or fewer.

c) Mean (Expected Value): This represents the average number of trials needed to achieve the first success.

d) Variance: This measures the spread of the distribution.

e) Standard Deviation: This is the square root of the variance and provides another measure of the distribution’s spread.

5. Read the Interpretation
The calculator provides a brief explanation of the results, helping you understand what the numbers mean in context.

6. Experiment with Different Values
Feel free to change the probability of success or the number of trials to see how it affects the results. This can help you gain intuition about how the geometric distribution behaves under different conditions.

By following these steps and considering these points, you can effectively use the Geometric Distribution Calculator to solve probability problems, analyze scenarios involving repeated trials until first success, and gain deeper insights into this important probability distribution.