6.3 Probability Distributions

• A probability distribution is a mathematical function that describes the likelihood of different outcomes of a random variable.
• A discrete probability distribution uses a probability density function (PDF) to describe probabilities.

  False
• An example of a discrete probability distribution is the number of heads when flipping a coin three times.
• A continuous probability distribution uses a probability density function (PDF) to describe probabilities within a range.
• A probability distribution can only be discrete.

  False
• The Bernoulli distribution describes the probability of success or failure in a single trial.
• The binomial distribution models the number of successes in a fixed number of independent trials.
• The Poisson distribution models the number of events occurring in a fixed interval of time or space.
• The normal distribution is characterized by a bell-shaped curve.
• The exponential distribution describes the time between events in a Poisson process.
• Arrange the following distributions based on whether they are discrete or continuous:

  1️⃣ Bernoulli

  2️⃣ Binomial

  3️⃣ Poisson

  4️⃣ Normal

  5️⃣ Exponential
• A discrete probability distribution assigns probabilities to a countable set of outcomes.
• The probability mass function (PMF) is used in continuous distributions.

  False
• The Bernoulli distribution is used to describe the probability of success or failure in a single trial.
• The binomial distribution is used to model the number of successes in a fixed number of independent trials.
• The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space.
• The Bernoulli distribution represents the probability of success or failure in a single trial.
• The binomial distribution is used to model the number of successes in a fixed number of independent trials.
• The Poisson distribution models the number of events occurring in a fixed interval of time or space.
• Continuous probability distributions use a probability density function (PDF) to describe probabilities.
• The normal distribution is characterized by its mean and standard deviation.
• The exponential distribution models the time between events in a Poisson process.
• The binomial distribution represents the number of successes in a fixed number of independent trials
• The Poisson distribution models the number of events occurring in a fixed interval of time or space
• Continuous probability distributions use a probability density function (PDF) to describe probabilities.
• Match the distribution with its parameters:

  Normal ↔️ Mean, Standard Deviation

  Exponential ↔️ Rate Parameter

  Uniform ↔️ Lower, Upper Limits
• The exponential distribution models the time between events in a Poisson process.
• The uniform distribution assigns equal probability to all values within a range.
• What is the shape of the normal distribution?

  Bell-shaped curve
• What are the parameters of the exponential distribution?

  Rate Parameter
• Continuous probability distributions use a probability density function (PDF) to describe probabilities
• The mean of a probability distribution is the average value.
• The median of a probability distribution is the middle value.
• The most frequent value in a probability distribution is called the mode
• What does the standard deviation of a probability distribution measure?

  Spread or variability
• The median of a discrete distribution is the middle value of x.
• What is the median of the coin flipping example in the study material?

  1
• The mode of a probability distribution is the value with the highest probability
• The standard deviation of a continuous distribution uses an integral to calculate its value.
• What is the difference between discrete and continuous probability distributions?

  Specific vs any values