6.3 Probability Distributions

• Match the probability distribution with its description:

  Discrete ↔️ Finite set of distinct values

  Continuous ↔️ Any value within a range
• What type of values can a random variable take in a discrete probability distribution?

  Specific integer values
• A probability mass function (PMF) is used for discrete probability distributions.


  True
• Discrete probability distributions describe the probability of a random variable taking on specific integer values only.


  True
• A probability distribution describes the possible values a random variable can take and their associated probabilities
• A continuous probability distribution describes the probability of a random variable taking on any value within a continuous range.


  True
• Match the characteristic with the type of probability distribution:

  Discrete ↔️ PMF

  Continuous ↔️ PDF
• Distributions describe the probability of a random variable taking on any value within a continuous range
• Discrete distributions use a probability mass function (PMF), while continuous distributions use a probability density function PDF
• What is the formula for the binomial probability mass function (PMF)?

  $P(X = x) =$$\binom{n}{x} p^{x} (1 - p)^{n - x}$
• What does p represent in the binomial probability formula?

  Probability of success
• Which type of probability distribution is associated with discrete random variables?

  Binomial
• Discrete probability distributions describe the probability of a random variable taking on a finite set of distinct values.


  True
• What is the normalization property of probability distributions?

  Sum of probabilities equals 1
• Discrete probability distributions describe the probability of a random variable taking on a finite set of distinct values
• Order the key differences between discrete and continuous probability distributions:

  1️⃣ Random variable takes on finite values

  2️⃣ Random variable can take on any value within a range

  3️⃣ PMF is used for discrete distributions

  4️⃣ PDF is used for continuous distributions
• What type of probability distribution is the binomial distribution?

  Discrete
• The binomial distribution can be contrasted with the continuous normal distribution.

  True
• What is the value of 'p' in the binomial distribution formula?

  Probability of success
• In the binomial distribution, 'n' represents the fixed number of independent trials
• In the normal distribution, the mean is represented by the symbol $μ$
• The probability density function (PDF) for the normal distribution is given by $f(x)$
• What type of tables are commonly used to find probabilities in the normal distribution?

  Standard normal tables
• What is a probability distribution?

  Mathematical function for probabilities
• The normal distribution is an example of a continuous probability distribution.


  True
• Match the probability distribution type with its example:

  Discrete ↔️ Binomial

  Continuous ↔️ Normal
• What is an example of a continuous probability distribution?

  Normal
• The binomial distribution models the probability of a random variable taking on a finite set of distinct values
• The binomial distribution is a type of discrete probability distribution that models the probability of a random variable taking on a finite set of distinct integer values
• What does 'n' represent in the binomial distribution?

  Number of independent trials
• The mean of the normal distribution is the center of the distribution.


  True
• The normal distribution is discrete, unlike the binomial distribution.

  False
• What is the probability $P(Z < - 1)$ from standard normal tables?


  0.1587
• Match the parameter with the distribution:

  Binomial ↔️ n and p

  Normal ↔️ μ and σ
• The binomial distribution models the probability of successes in a fixed number of independent trials
• What is a probability distribution?

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

  Binomial distribution
• A continuous probability distribution allows the random variable to take on any real value within a specified range
• What is the key difference between discrete and continuous probability distributions in terms of variable values?

  Finite vs. continuous values
• Match the type of distribution with its example:

  Discrete ↔️ Binomial

  Continuous ↔️ Normal