4.1 Probability Distributions

• What is a probability distribution?

  A mathematical function
• What is an example of a continuous distribution?

  Height of students
• What represents probabilities in continuous distributions?

  Area under a curve
• The binomial distribution requires the number of trials and the probability of success as parameters.
• The geometric distribution models the number of trials until the first success.

  True
• The geometric distribution requires the parameter: probability of success
• What are the two types of probability distributions?

  Discrete and continuous
• What must the probabilities assigned to each possible value in a discrete distribution sum to?

  1
• What is the formula to calculate the probability of exactly x successes in n trials using the binomial distribution?

  $P(X = x) =$$\binom{n}{x} p^{x} (1 - p)^{n - x}$
• If a fair coin is flipped 5 times, the probability of success (p) is 0.5.
• What does 'n' represent in the binomial distribution formula?

  Number of trials
• What does 'n' stand for in the binomial distribution formula?

  Number of trials
• What is the value of 'x' in the Poisson distribution example?

  5
• What is the main difference between discrete and continuous distributions in terms of value range?

  Countable vs. any value
• The exponential distribution models the time between events
• In a discrete distribution, values can only take specific, countable values.

  True
• What is the key parameter in the geometric distribution?

  Probability of success
• What are the key parameters of the binomial distribution?

  n and p
• Steps to calculate probabilities using the binomial distribution

  1️⃣ Identify the number of trials (n)

  2️⃣ Identify the number of successes (x)

  3️⃣ Identify the probability of success (p)

  4️⃣ Plug values into the binomial formula
• What does 'n' represent in the binomial distribution formula?

  Number of trials
• Continuous probability distributions allow random variables to take on any value within a range.


  True
• Discrete and continuous are the two types of probability distributions.


  True
• In discrete distributions, the probabilities for each possible value must sum to 1.


  True
• The normal distribution is an example of a continuous distribution.


  True
• Discrete distributions are used for random variables that can only take specific, countable values.


  True
• A discrete probability distribution assigns probabilities to specific, countable values.
• Match the discrete distribution with its defining characteristic:

  Binomial ↔️ Fixed number of trials

  Poisson ↔️ Events in fixed interval

  Geometric ↔️ Trials until first success
• The parameter n in the binomial formula represents the number of trials.


  True
• The probability of getting exactly 3 heads in 5 coin flips is 31.25%.

  True
• The probability of getting exactly 3 heads in 5 coin flips is 0.3125.


  True
• The probability of getting exactly 3 heads in 5 coin flips is 31.25%.


  True
• The probability of exactly 5 customers arriving in an hour is approximately 0.1008.


  True
• Match the type of distribution with its example:

  Discrete ↔️ Binomial

  Continuous ↔️ Normal
• What is a probability distribution?

  Assigns probabilities to values
• Steps to define a discrete probability distribution

  1️⃣ Identify possible values

  2️⃣ Assign probabilities to each value

  3️⃣ Ensure probabilities sum to 1
• The three key discrete probability distributions are binomial, Poisson, and geometric
• The Poisson distribution assumes a constant average rate of events.


  True
• The probability of getting exactly 3 heads in 5 coin flips is approximately 0.3125
• Match the parameter with its description in the Poisson distribution:

  x ↔️ Number of events

  λ ↔️ Average rate of events
• How are probabilities represented in continuous distributions?

  Area under a curve