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Questions and Answers
What are the two requirements for a discrete probability distribution?
What are the two requirements for a discrete probability distribution?
The sum of the probabilities must equal 1, and each probability must be between 0 and 1, inclusive.
Determine whether the following random variable is discrete or continuous and state the possible values: (a) The number of points scored during a basketball game.
Determine whether the following random variable is discrete or continuous and state the possible values: (a) The number of points scored during a basketball game.
Discrete; possible values are x = 0, 1, 2, ...
Determine whether the following random variable is discrete or continuous and state the possible values: (b) The time it takes to fly from City A to City B.
Determine whether the following random variable is discrete or continuous and state the possible values: (b) The time it takes to fly from City A to City B.
Continuous; possible values are t > 0.
Determine whether the following random variable is discrete or continuous and state the possible values: (a) The number of people in a restaurant that has a capacity of 300.
Determine whether the following random variable is discrete or continuous and state the possible values: (a) The number of people in a restaurant that has a capacity of 300.
Determine whether the following random variable is discrete or continuous and state the possible values: (b) The distance a baseball travels in the air after being hit.
Determine whether the following random variable is discrete or continuous and state the possible values: (b) The distance a baseball travels in the air after being hit.
Is the distribution a discrete probability distribution based on the following values: (0, 0.07), (1, 0.34), (2, 0.27), (3, 0.15), (4, 0.17)?
Is the distribution a discrete probability distribution based on the following values: (0, 0.07), (1, 0.34), (2, 0.27), (3, 0.15), (4, 0.17)?
Determine the required value of the missing probability P(4) to make the following distribution a discrete probability distribution: (3, 0.34), (4, ?), (5, 0.08), (6, 0.29).
Determine the required value of the missing probability P(4) to make the following distribution a discrete probability distribution: (3, 0.34), (4, ?), (5, 0.08), (6, 0.29).
Is the following distribution a discrete probability distribution based on the values: (0, 0.263), (1, 0.576), (2, 0.127), (3, 0.029), (4, 0.004), (5, 0.001)?
Is the following distribution a discrete probability distribution based on the values: (0, 0.263), (1, 0.576), (2, 0.127), (3, 0.029), (4, 0.004), (5, 0.001)?
Describe the shape of the distribution represented by the random variable X for the number of marriages an individual aged 15 years or older has been involved in.
Describe the shape of the distribution represented by the random variable X for the number of marriages an individual aged 15 years or older has been involved in.
Flashcards
Discrete Probability Distribution Requirements
Discrete Probability Distribution Requirements
For a distribution to be discrete, the sum of the probabilities must equal 1, and each probability must be between 0 and 1, inclusive.
Discrete Random Variable Example (Basketball)
Discrete Random Variable Example (Basketball)
The number of points scored in a basketball game is a discrete random variable. Possible values range from 0 to a theoretically infinite number of points.
Continuous Random Variable Example (Flight Time)
Continuous Random Variable Example (Flight Time)
The time it takes to fly from City A to City B is a continuous random variable, with possible values greater than zero.
Discrete Random Variable Example (Restaurant Capacity)
Discrete Random Variable Example (Restaurant Capacity)
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Continuous Random Variable Example (Baseball Distance)
Continuous Random Variable Example (Baseball Distance)
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Discrete Probability Distribution Example (Basketball Scores)
Discrete Probability Distribution Example (Basketball Scores)
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Missing Probability Calculation
Missing Probability Calculation
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Distribution Validity (Example 1)
Distribution Validity (Example 1)
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Distribution Shape (Marriages)
Distribution Shape (Marriages)
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Study Notes
Discrete Probability Distribution Requirements
- The sum of all probabilities must equal 1: ∑ P(x) = 1.
- Each probability must lie within the range 0 to 1, inclusive: 0 ≤ P(x) ≤ 1.
Random Variable Classification
- Random variables can be classified as discrete or continuous.
- Discrete Example: Number of points scored in a basketball game. Possible values: x = 0, 1, 2, ...
- Continuous Example: Time taken to fly between two cities. Possible values: t > 0.
Additional Random Variable Examples
- Discrete Example: Number of people in a restaurant with a capacity of 300. Possible values: x = 0, 1, 2, ..., 300.
- Continuous Example: Distance a baseball travels after being hit. Possible values: d > 0.
Validating Discrete Probability Distribution
- A given distribution of probabilities is valid if:
- The sum equals 1.
- All probabilities are between 0 and 1.
- Example probabilities:
- x = 0, P(x) = 0.07
- x = 1, P(x) = 0.34
- Sum = 1 confirms validity.
Finding Missing Probability
- In a probability distribution, if a value is missing, calculate it by ensuring the total equals 1.
- Example:
- Given P(3) = 0.34, P(5) = 0.08, P(6) = 0.29.
- Total given = 0.71, thus P(4) = 1.00 - 0.71 = 0.29.
Analyzing a Specific Probability Distribution
- Example distribution for marriages:
- x = 0, P(x) = 0.263
- x = 1, P(x) = 0.576
- x = 2, P(x) = 0.127
- x = 3, P(x) = 0.029
- x = 4, P(x) = 0.004
- x = 5, P(x) = 0.001
- Verification:
- All probabilities are between 0 and 1.
- Sum of probabilities = 1, confirming it’s a discrete probability distribution.
- Graph Characteristics:
- The distribution is unimodal (one mode) and skewed right.
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