6.3 Probability Distributions

Cards (76)

  • What is the probability sum or integral equal to in a continuous probability distribution?
    \int P(x) dx = 1</latex>
  • What is a discrete probability distribution?
    Probabilities assigned to discrete values
  • What is the sum of probabilities in a discrete probability distribution?
    1
  • What expression represents the sum of probabilities in a discrete probability distribution?
    \sum P(x) = 1</latex>
  • Probabilities in a discrete probability distribution are assigned to continuous values of the random variable.
    False
  • What is the probability expression for a continuous probability distribution?
    ∫P(x)dx=\int P(x) dx =1 1
  • What is the mathematical expression that describes the sum of probabilities in a continuous probability distribution?
    ∫P(x)dx=\int P(x) dx =1 1
  • When rolling a fair six-sided die, what is the probability of rolling a 3?
    1/6
  • In the binomial distribution, \( n \) represents the number of independent trials.
  • The area under the PDF of a continuous probability distribution over its entire range must equal 1.
  • What type of probability distribution assigns probabilities to discrete, countable values of a random variable?
    Discrete
  • What is the expression for the sum of probabilities in a discrete probability distribution?
    ∑P(x)=\sum P(x) =1 1
  • Match the type of probability distribution with its definition:
    Discrete Probability Distribution ↔️ Probabilities assigned to discrete values
    Continuous Probability Distribution ↔️ Probabilities defined over a continuous range
  • In a discrete probability distribution, the sum of all probabilities must equal 1.

    True
  • What does \( n \) represent in the Binomial distribution?
    Number of trials
  • What does the mean (μ) of a normal distribution represent?
    The central value
  • Once we have the z-score, we use z-tables or calculators
  • The continuous probability distribution integrates to 1
  • What is a probability distribution?
    Assigns probabilities to random variables
  • What is an example of a continuous probability distribution?
    Heights of students
  • Probabilities in a discrete probability distribution are assigned to specific discrete values of a random variable
  • A discrete probability distribution is a probability distribution where probabilities are assigned to discrete values of a random variable.
  • The probabilities in a discrete probability distribution must sum to 1.

    True
  • The probabilities in a continuous probability distribution must integrate to 1.

    True
  • What are the main differences between discrete and continuous probability distributions?
    Discrete values vs. range
  • In a continuous probability distribution, the probabilities must integrate to 1 over the entire range.
  • A continuous probability distribution uses a Probability Density Function (PDF) to describe likelihoods.

    True
  • A probability distribution is a mathematical function that assigns probabilities to each possible value of a random variable.
    True
  • What is the probability of rolling a 3 on a fair 6-sided die?
    1/6
  • The total sum of probabilities in a discrete probability distribution is always equal to 1.

    True
  • What is the expression for the total area under the curve in a continuous probability distribution?
    \int P(x) dx = 1</latex>
  • What is the formula for calculating the probability in a Binomial distribution?
    P(X=k)=P(X = k) =(nk)pk(1−p)n−k {n \choose k} p^{k} (1 - p)^{n - k}
  • What is the function called that assigns relative likelihoods to each value in a continuous probability distribution?
    PDF
  • The normal distribution is bell-shaped and symmetric around the mean
  • To work with normal distributions, we often convert values to a z-score
  • In a continuous probability distribution, the probabilities must integrate to 1
  • Rolling a die is an example of a discrete probability distribution.

    True
  • The probabilities in a discrete probability distribution must sum to 1.

    True
  • In a discrete probability distribution, probabilities are assigned to specific discrete values of the random variable.

    True
  • What expression represents the integral of probabilities in a continuous probability distribution?
    ∫P(x)dx=\int P(x) dx =1 1