Overview
This lecture explains the difference between the binomial PDF and CDF calculator functions, focusing on when and how to use each for probability problems.
Binomial PDF (Probability Distribution Function)
- Binomial PDF is used to find the probability of exactly one specified outcome for a given number of trials.
- Syntax: binomPDF(n, p, x) calculates the probability of getting exactly x successes.
- Example: To find the probability of getting exactly 3 tails in 10 coin tosses (p = 0.5), use binomPDF(10, 0.5, 3).
Binomial CDF (Cumulative Distribution Function)
- Binomial CDF calculates the probability of obtaining a value less than or equal to a specific number of successes.
- Syntax: binomCDF(n, p, x) finds the probability of getting x or fewer successes (from 0 up to x).
- Example: binomCDF(10, 0.5, 3) gives the probability of getting 3 or fewer tails in 10 tosses.
- CDF is more convenient for cumulative probabilities compared to calculating several PDFs and adding them.
- Use CDF for phrases like "no more than X" or "at most X" (less than or equal to X).
- For "exactly X," always use PDF.
Choosing PDF vs. CDF
- Use PDF for exactly one outcome (e.g., exactly 6 tails).
- Use CDF for a range up to a certain number (e.g., no more than 7 tails).
- For "at least" or "more than" scenarios, consider using the complement rule with CDF.
Key Terms & Definitions
- Binomial PDF — Probability of exactly a specified number of successes in a set of trials.
- Binomial CDF — Probability of having up to and including a specified number of successes.
- Complement Rule — Using the probability of the opposite event to find a desired probability.
Action Items / Next Steps
- Add binomCDF (Cumulative Distribution Function) to your calculator notes.
- Practice using both binomPDF and binomCDF functions for different probability scenarios.
- Review the complement rule for probabilities involving "at least" or "more than."