Discrete Probability Distribution Examples for Pre-Calculus Students

📚 Quick Study Guide

• 🎲 Discrete probability distributions deal with countable outcomes.
• 📊 Each outcome has a probability between 0 and 1.
• ➕ The sum of all probabilities equals 1.
• 💡 Common examples include the Bernoulli, Binomial, and Poisson distributions.
• ✏️ The probability mass function (PMF) gives the probability of each outcome.
• 💰 Expected value is the average outcome, calculated as $\sum xP(x)$.

🧪 Practice Quiz

1. What is a key characteristic of a discrete probability distribution?
   1. It deals with continuous variables.
   2. The sum of all probabilities must equal 1.
   3. Probabilities can be negative.
   4. It only applies to normally distributed data.


2. Which of the following is an example of a discrete random variable?
   1. The height of a student.
   2. The temperature of a room.
   3. The number of cars passing a point on a highway in an hour.
   4. The weight of a bag of apples.


3. What does the probability mass function (PMF) provide?
   1. The cumulative probability up to a certain point.
   2. The probability of each outcome.
   3. The expected value of the distribution.
   4. The variance of the distribution.


4. In a Bernoulli distribution, what does 'success' typically represent?
   1. A failure.
   2. The outcome of interest.
   3. The average outcome.
   4. An impossible event.


5. If $P(x) = 0.2$ for all $x$, and there are 5 possible values for $x$, is this a valid discrete probability distribution?
   1. Yes
   2. No, because probabilities must be unique.
   3. No, because the probabilities do not sum to 1.
   4. Yes, if the variable is continuous.


6. What is the expected value of a discrete probability distribution?
   1. The most frequent outcome.
   2. The average outcome.
   3. The median outcome.
   4. The square root of the variance.


7. Which distribution is most suitable for modeling the number of events occurring in a fixed interval of time or space?
   1. Binomial distribution.
   2. Normal distribution.
   3. Poisson distribution.
   4. Uniform distribution.